{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Mixed Effects Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:39.131409Z",
     "iopub.status.busy": "2023-12-14T14:40:39.131165Z",
     "iopub.status.idle": "2023-12-14T14:40:44.347005Z",
     "shell.execute_reply": "2023-12-14T14:40:44.345143Z"
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   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "from statsmodels.tools.sm_exceptions import ConvergenceWarning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: The R code and the results in this notebook has been converted to markdown so that R is not required to build the documents. The R results in the notebook were computed using R 3.5.1 and lme4 1.1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%load_ext rpy2.ipython\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R library(lme4)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "array(['lme4', 'Matrix', 'tools', 'stats', 'graphics', 'grDevices',\n",
    "       'utils', 'datasets', 'methods', 'base'], dtype='<U9')\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing R lmer to statsmodels MixedLM\n",
    "=======================================\n",
    "\n",
    "The statsmodels implementation of linear mixed models (MixedLM) closely follows the approach outlined in Lindstrom and Bates (JASA 1988).  This is also the approach followed in the  R package LME4.  Other packages such as Stata, SAS, etc. should also be consistent with this approach, as the basic techniques in this area are mostly mature.\n",
    "\n",
    "Here we show how linear mixed models can be fit using the MixedLM procedure in statsmodels.  Results from R (LME4) are included for comparison.\n",
    "\n",
    "Here are our import statements:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Growth curves of pigs\n",
    "\n",
    "These are longitudinal data from a factorial experiment. The outcome variable is the weight of each pig, and the only predictor variable we will use here is \"time\".  First we fit a model that expresses the mean weight as a linear function of time, with a random intercept for each pig. The model is specified using formulas. Since the random effects structure is not specified, the default random effects structure (a random intercept for each group) is automatically used. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:44.352968Z",
     "iopub.status.busy": "2023-12-14T14:40:44.350991Z",
     "iopub.status.idle": "2023-12-14T14:40:45.817792Z",
     "shell.execute_reply": "2023-12-14T14:40:45.816879Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Mixed Linear Model Regression Results\n",
      "========================================================\n",
      "Model:            MixedLM Dependent Variable: Weight    \n",
      "No. Observations: 861     Method:             REML      \n",
      "No. Groups:       72      Scale:              11.3669   \n",
      "Min. group size:  11      Log-Likelihood:     -2404.7753\n",
      "Max. group size:  12      Converged:          Yes       \n",
      "Mean group size:  12.0                                  \n",
      "--------------------------------------------------------\n",
      "             Coef.  Std.Err.    z    P>|z| [0.025 0.975]\n",
      "--------------------------------------------------------\n",
      "Intercept    15.724    0.788  19.952 0.000 14.179 17.268\n",
      "Time          6.943    0.033 207.939 0.000  6.877  7.008\n",
      "Group Var    40.395    2.149                            \n",
      "========================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "data = sm.datasets.get_rdataset(\"dietox\", \"geepack\").data\n",
    "md = smf.mixedlm(\"Weight ~ Time\", data, groups=data[\"Pig\"])\n",
    "mdf = md.fit(method=[\"lbfgs\"])\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the same model fit in R using LMER:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%%R\n",
    "data(dietox, package='geepack')\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R print(summary(lmer('Weight ~ Time + (1|Pig)', data=dietox)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: Weight ~ Time + (1 | Pig)\n",
    "   Data: dietox\n",
    "\n",
    "REML criterion at convergence: 4809.6\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-4.7118 -0.5696 -0.0943  0.4877  4.7732 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance Std.Dev.\n",
    " Pig      (Intercept) 40.39    6.356   \n",
    " Residual             11.37    3.371   \n",
    "Number of obs: 861, groups:  Pig, 72\n",
    "\n",
    "Fixed effects:\n",
    "            Estimate Std. Error t value\n",
    "(Intercept) 15.72352    0.78805   19.95\n",
    "Time         6.94251    0.03339  207.94\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time -0.275\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that in the statsmodels summary of results, the fixed effects and random effects parameter estimates are shown in a single table.  The random effect for animal is labeled \"Intercept RE\" in the statsmodels output above.  In the LME4 output, this effect is the pig intercept under the random effects section.\n",
    "\n",
    "There has been a lot of debate about whether the standard errors for random effect variance and covariance parameters are useful.  In LME4, these standard errors are not displayed, because the authors of the package believe they are not very informative.  While there is good reason to question their utility, we elected to include the standard errors in the summary table, but do not show the corresponding Wald confidence intervals.\n",
    "\n",
    "Next we fit a model with two random effects for each animal: a random intercept, and a random slope (with respect to time).  This means that each pig may have a different baseline weight, as well as growing at a different rate. The formula specifies that \"Time\" is a covariate with a random coefficient.  By default, formulas always include an intercept (which could be suppressed here using \"0 + Time\" as the formula)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:45.826125Z",
     "iopub.status.busy": "2023-12-14T14:40:45.823535Z",
     "iopub.status.idle": "2023-12-14T14:40:47.010155Z",
     "shell.execute_reply": "2023-12-14T14:40:47.007772Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mixed Linear Model Regression Results\n",
      "===========================================================\n",
      "Model:             MixedLM  Dependent Variable:  Weight    \n",
      "No. Observations:  861      Method:              REML      \n",
      "No. Groups:        72       Scale:               6.0372    \n",
      "Min. group size:   11       Log-Likelihood:      -2217.0475\n",
      "Max. group size:   12       Converged:           Yes       \n",
      "Mean group size:   12.0                                    \n",
      "-----------------------------------------------------------\n",
      "                 Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
      "-----------------------------------------------------------\n",
      "Intercept        15.739    0.550 28.603 0.000 14.660 16.817\n",
      "Time              6.939    0.080 86.925 0.000  6.783  7.095\n",
      "Group Var        19.503    1.561                           \n",
      "Group x Time Cov  0.294    0.153                           \n",
      "Time Var          0.416    0.033                           \n",
      "===========================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "md = smf.mixedlm(\"Weight ~ Time\", data, groups=data[\"Pig\"], re_formula=\"~Time\")\n",
    "mdf = md.fit(method=[\"lbfgs\"])\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the same model fit using LMER in R:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R print(summary(lmer(\"Weight ~ Time + (1 + Time | Pig)\", data=dietox)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: Weight ~ Time + (1 + Time | Pig)\n",
    "   Data: dietox\n",
    "\n",
    "REML criterion at convergence: 4434.1\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-6.4286 -0.5529 -0.0416  0.4841  3.5624 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance Std.Dev. Corr\n",
    " Pig      (Intercept) 19.493   4.415        \n",
    "          Time         0.416   0.645    0.10\n",
    " Residual              6.038   2.457        \n",
    "Number of obs: 861, groups:  Pig, 72\n",
    "\n",
    "Fixed effects:\n",
    "            Estimate Std. Error t value\n",
    "(Intercept) 15.73865    0.55012   28.61\n",
    "Time         6.93901    0.07982   86.93\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time 0.006 \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The random intercept and random slope are only weakly correlated $(0.294 / \\sqrt{19.493 * 0.416} \\approx 0.1)$.  So next we fit a model in which the two random effects are constrained to be uncorrelated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:47.015837Z",
     "iopub.status.busy": "2023-12-14T14:40:47.013851Z",
     "iopub.status.idle": "2023-12-14T14:40:47.030427Z",
     "shell.execute_reply": "2023-12-14T14:40:47.029633Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10324316832591753"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.294 / (19.493 * 0.416) ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:47.034153Z",
     "iopub.status.busy": "2023-12-14T14:40:47.033566Z",
     "iopub.status.idle": "2023-12-14T14:40:48.288784Z",
     "shell.execute_reply": "2023-12-14T14:40:48.287827Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mixed Linear Model Regression Results\n",
      "===========================================================\n",
      "Model:             MixedLM  Dependent Variable:  Weight    \n",
      "No. Observations:  861      Method:              REML      \n",
      "No. Groups:        72       Scale:               6.0283    \n",
      "Min. group size:   11       Log-Likelihood:      -2217.3481\n",
      "Max. group size:   12       Converged:           Yes       \n",
      "Mean group size:   12.0                                    \n",
      "-----------------------------------------------------------\n",
      "                 Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
      "-----------------------------------------------------------\n",
      "Intercept        15.739    0.554 28.388 0.000 14.652 16.825\n",
      "Time              6.939    0.080 86.248 0.000  6.781  7.097\n",
      "Group Var        19.837    1.571                           \n",
      "Group x Time Cov  0.000    0.000                           \n",
      "Time Var          0.423    0.033                           \n",
      "===========================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "md = smf.mixedlm(\"Weight ~ Time\", data, groups=data[\"Pig\"], re_formula=\"~Time\")\n",
    "free = sm.regression.mixed_linear_model.MixedLMParams.from_components(\n",
    "    np.ones(2), np.eye(2)\n",
    ")\n",
    "\n",
    "mdf = md.fit(free=free, method=[\"lbfgs\"])\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The likelihood drops by 0.3 when we fix the correlation parameter to 0.  Comparing 2 x 0.3 = 0.6 to the chi^2 1 df reference distribution suggests that the data are very consistent with a model in which this parameter is equal to 0.\n",
    "\n",
    "Here is the same model fit using LMER in R (note that here R is reporting the REML criterion instead of the likelihood, where the REML criterion is twice the log likelihood):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R print(summary(lmer(\"Weight ~ Time + (1 | Pig) + (0 + Time | Pig)\", data=dietox)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: Weight ~ Time + (1 | Pig) + (0 + Time | Pig)\n",
    "   Data: dietox\n",
    "\n",
    "REML criterion at convergence: 4434.7\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-6.4281 -0.5527 -0.0405  0.4840  3.5661 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance Std.Dev.\n",
    " Pig      (Intercept) 19.8404  4.4543  \n",
    " Pig.1    Time         0.4234  0.6507  \n",
    " Residual              6.0282  2.4552  \n",
    "Number of obs: 861, groups:  Pig, 72\n",
    "\n",
    "Fixed effects:\n",
    "            Estimate Std. Error t value\n",
    "(Intercept) 15.73875    0.55444   28.39\n",
    "Time         6.93899    0.08045   86.25\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time -0.086\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sitka growth data\n",
    "\n",
    "This is one of the example data sets provided in the LMER R library.  The outcome variable is the size of the tree, and the covariate used here is a time value.  The data are grouped by tree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:48.296506Z",
     "iopub.status.busy": "2023-12-14T14:40:48.294167Z",
     "iopub.status.idle": "2023-12-14T14:40:48.802018Z",
     "shell.execute_reply": "2023-12-14T14:40:48.800941Z"
    }
   },
   "outputs": [],
   "source": [
    "data = sm.datasets.get_rdataset(\"Sitka\", \"MASS\").data\n",
    "endog = data[\"size\"]\n",
    "data[\"Intercept\"] = 1\n",
    "exog = data[[\"Intercept\", \"Time\"]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the statsmodels LME fit for a basic model with a random intercept.  We are passing the endog and exog data directly to the LME init function as arrays.  Also note that endog_re is specified explicitly in argument 4 as a random intercept (although this would also be the default if it were not specified)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:48.805446Z",
     "iopub.status.busy": "2023-12-14T14:40:48.805177Z",
     "iopub.status.idle": "2023-12-14T14:40:49.928986Z",
     "shell.execute_reply": "2023-12-14T14:40:49.928296Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Mixed Linear Model Regression Results\n",
      "=======================================================\n",
      "Model:             MixedLM Dependent Variable: size    \n",
      "No. Observations:  395     Method:             REML    \n",
      "No. Groups:        79      Scale:              0.0392  \n",
      "Min. group size:   5       Log-Likelihood:     -82.3884\n",
      "Max. group size:   5       Converged:          Yes     \n",
      "Mean group size:   5.0                                 \n",
      "-------------------------------------------------------\n",
      "              Coef. Std.Err.   z    P>|z| [0.025 0.975]\n",
      "-------------------------------------------------------\n",
      "Intercept     2.273    0.088 25.864 0.000  2.101  2.446\n",
      "Time          0.013    0.000 47.796 0.000  0.012  0.013\n",
      "Intercept Var 0.374    0.345                           \n",
      "=======================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "md = sm.MixedLM(endog, exog, groups=data[\"tree\"], exog_re=exog[\"Intercept\"])\n",
    "mdf = md.fit()\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the same model fit in R using LMER:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R\n",
    "data(Sitka, package=\"MASS\")\n",
    "print(summary(lmer(\"size ~ Time + (1 | tree)\", data=Sitka)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: size ~ Time + (1 | tree)\n",
    "   Data: Sitka\n",
    "\n",
    "REML criterion at convergence: 164.8\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-2.9979 -0.5169  0.1576  0.5392  4.4012 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance Std.Dev.\n",
    " tree     (Intercept) 0.37451  0.612   \n",
    " Residual             0.03921  0.198   \n",
    "Number of obs: 395, groups:  tree, 79\n",
    "\n",
    "Fixed effects:\n",
    "             Estimate Std. Error t value\n",
    "(Intercept) 2.2732443  0.0878955   25.86\n",
    "Time        0.0126855  0.0002654   47.80\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time -0.611\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now try to add a random slope.  We start with R this time.  From the code and output below we see that the REML estimate of the variance of the random slope is nearly zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R print(summary(lmer(\"size ~ Time + (1 + Time | tree)\", data=Sitka)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: size ~ Time + (1 + Time | tree)\n",
    "   Data: Sitka\n",
    "\n",
    "REML criterion at convergence: 153.4\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-2.7609 -0.5173  0.1188  0.5270  3.5466 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance  Std.Dev. Corr \n",
    " tree     (Intercept) 2.217e-01 0.470842      \n",
    "          Time        3.288e-06 0.001813 -0.17\n",
    " Residual             3.634e-02 0.190642      \n",
    "Number of obs: 395, groups:  tree, 79\n",
    "\n",
    "Fixed effects:\n",
    "            Estimate Std. Error t value\n",
    "(Intercept) 2.273244   0.074655   30.45\n",
    "Time        0.012686   0.000327   38.80\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time -0.615\n",
    "convergence code: 0\n",
    "Model failed to converge with max|grad| = 0.793203 (tol = 0.002, component 1)\n",
    "Model is nearly unidentifiable: very large eigenvalue\n",
    " - Rescale variables?\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we run this in statsmodels LME with defaults, we see that the variance estimate is indeed very small, which leads to a warning about the solution being on the boundary of the parameter space.  The regression slopes agree very well with R, but the likelihood value is much higher than that returned by R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:49.933547Z",
     "iopub.status.busy": "2023-12-14T14:40:49.932493Z",
     "iopub.status.idle": "2023-12-14T14:40:55.956409Z",
     "shell.execute_reply": "2023-12-14T14:40:55.955481Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/statsmodels/regression/mixed_linear_model.py:2238: ConvergenceWarning: The MLE may be on the boundary of the parameter space.\n",
      "  warnings.warn(msg, ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             Mixed Linear Model Regression Results\n",
      "===============================================================\n",
      "Model:               MixedLM    Dependent Variable:    size    \n",
      "No. Observations:    395        Method:                REML    \n",
      "No. Groups:          79         Scale:                 0.0264  \n",
      "Min. group size:     5          Log-Likelihood:        -62.4834\n",
      "Max. group size:     5          Converged:             Yes     \n",
      "Mean group size:     5.0                                       \n",
      "---------------------------------------------------------------\n",
      "                     Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
      "---------------------------------------------------------------\n",
      "Intercept             2.273    0.101 22.513 0.000  2.075  2.471\n",
      "Time                  0.013    0.000 33.888 0.000  0.012  0.013\n",
      "Intercept Var         0.646    0.914                           \n",
      "Intercept x Time Cov -0.001    0.003                           \n",
      "Time Var              0.000    0.000                           \n",
      "===============================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "exog_re = exog.copy()\n",
    "md = sm.MixedLM(endog, exog, data[\"tree\"], exog_re)\n",
    "mdf = md.fit()\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can further explore the random effects structure by constructing plots of the profile likelihoods. We start with the random intercept, generating a plot of the profile likelihood from 0.1 units below to 0.1 units above the MLE. Since each optimization inside the profile likelihood generates a warning (due to the random slope variance being close to zero), we turn off the warnings here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:40:55.964351Z",
     "iopub.status.busy": "2023-12-14T14:40:55.962546Z",
     "iopub.status.idle": "2023-12-14T14:41:15.366849Z",
     "shell.execute_reply": "2023-12-14T14:41:15.365975Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.filterwarnings(\"ignore\")\n",
    "    likev = mdf.profile_re(0, \"re\", dist_low=0.1, dist_high=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a plot of the profile likelihood function.  We multiply the log-likelihood difference by 2 to obtain the usual $\\chi^2$ reference distribution with 1 degree of freedom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:41:15.370654Z",
     "iopub.status.busy": "2023-12-14T14:41:15.370374Z",
     "iopub.status.idle": "2023-12-14T14:41:15.381582Z",
     "shell.execute_reply": "2023-12-14T14:41:15.380384Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:41:15.384738Z",
     "iopub.status.busy": "2023-12-14T14:41:15.384474Z",
     "iopub.status.idle": "2023-12-14T14:41:15.997876Z",
     "shell.execute_reply": "2023-12-14T14:41:15.997140Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '-2 times profile log likelihood')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 8))\n",
    "plt.plot(likev[:, 0], 2 * likev[:, 1])\n",
    "plt.xlabel(\"Variance of random intercept\", size=17)\n",
    "plt.ylabel(\"-2 times profile log likelihood\", size=17)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a plot of the profile likelihood function. The profile likelihood plot shows that the MLE of the random slope variance parameter is a very small positive number, and that there is low uncertainty in this estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:41:16.002439Z",
     "iopub.status.busy": "2023-12-14T14:41:16.001220Z",
     "iopub.status.idle": "2023-12-14T14:41:39.756204Z",
     "shell.execute_reply": "2023-12-14T14:41:39.755248Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CSi7DwFBPDAz1REGJBtviqqdAnk5XYcX+ZBSXV+Gtce15ADoRkRni6mMiojo4eD4XD686ClVZJSICXfDDzJ4sZ9QkmjkoMKVXc/z6bB+8P74jBAH49mgqXt16BjodJ8EQEZkbjqAREd3BzjNXMev7WGi0OvRt7Y4Vj3SBvYJ/fFLTm9A1AHKZgOc2xeH7Y6kQRRHv3NOBI2lERGaEP2EQEd3Gj8fT8PKWf6ATgZEdvLHsgU6wsZJLHYss2L2d/SETBMz7MRY/HE+DVidiyX0dWdKIiMwECxoR0S2s+jsZb+9IBAA80DUA79zbAXL+EExG4O4IPwgCMHdjLDbFXIFOBN4b35H/fhIRmQEWNCKi/yOKIpbuOofley8AAGb2C8b8Edw1j4zLuE5+kAkC5myMxU8nr0AURbw/IZwljYjIxLGgERH9h04nImpbPL45chkA8MJdIXhqQEuWMzJKY8J9IRMEzPrhFLacSodOFPHBhHBYybkHGBGRqWJBIyK6plKrw/Ob4vBLbAYEAXhrXHs83DNI6lhEtzWqow9kAvDs96ewNTYDOhH48H6WNCIiU8U/vYmIAJRptHj8mxj8EpsBK5mAjx+MYDkjkzGigw+WP9QZVjIB2+IyMGdjLKquHW5NRESmhQWNiCyeurwSU9Ycw56kbNhYyfDV5K4YG+4rdSyiehne3hufT+oMa7mA7f9cxewfYlHJkkZEZHJY0IjIouUWV+DBFUdwLCUfTjZW+GZ6DwwM9ZQ6FpFehrXzxheTukAhl2HH6auY9f0pljQiIhPDgkZEFiu9sAz3fxmNhKtquDko8P3MnujewlXqWEQNMqStF758pDMUchl+P5OJp789CU0VSxoRkalgQSMii3QhuxjjvziM5NwS+LnYYdMTkWjvp5Q6FpFBDAr1worJXaCwkmFXQhaeYkkjIjIZLGhEZHFOX1Hh/hXRuKoqR0sPB2x+MhLBHo5SxyIyqIEhnvhqclfYWMnwZ2IWntwQg4oqrdSxiIjoDljQiMiiHEnOw8SvjiC/RIMOfkpseqIXfJR2UsciahT923hg1ZTqkvZXUjae+CYG5ZUsaURExowFjYgsxl+JWZiy5hiKK6rQo4UrvnusB1wdFFLHImpUfVt7YM3UbrC1lmHv2Rw8zpJGRGTUWNCIyCJsPZWOmd/EoKJKhyFhnlg3rTucbK2ljkXUJHq3cq8tafvP5eCx9SdY0oiIjBQLGhGZvfXRKZizMRZanYh7IvzwxcNdYGstlzoWUZPq1dIdax/tDjtrOf4+n4vH1p9AmYYljYjI2LCgEZHZEkURn/51Hgt/iQcATO3VHEsnhMNazj/6yDL1DHbD2ke7wV5RXdJmrD/OkkZEZGT4UwoRmSWdTsTbOxKxdPc5AMDswa0RNaYtZDJB4mRE0uoR7IZ107rDQSHHoQt5mLb2OEo1VVLHIiKia1jQiMjsVGl1ePGnf7D64CUAwMLRbTF3aBsIAssZEQB0a+6K9dO7w9HGCtHJeXj06+MoqWBJIyIyBixoRGRWyiu1ePq7k9gccwVymYAPJoRjWp8WUsciMjpdgqpLmpONFY5eymdJIyIyEixoRGQ2iiuqMH3dcfwRnwWFXIbPJ3XG+C7+UsciMlqdA5vVlrRjKfm1x1AQEZF0WNCIyCwUlGgwadVRHLqQBweFHGsf7Ya72nlLHYvI6EUENsOGGT3gZGuFE5cLMGXNMRSVV0odi4jIYrGgEZHJy1KX44GV0YhLK4SLvTW+fawnerVylzoWkckID3DBtzN6wNnWCjGXCzB5zTGoWdKIiCTBgkZEJu1yXgnu++IwzmUVw8vZBpsej0SnABepYxGZnI7+LvjusZ5Q2lnjVGohHll9DKoyljQioqbGgkZEJivxqhrjv4zGlYIyBLnZY/MTvdDay0nqWEQmq72fEt/O6AEXe2vEpRVi8uqjLGlERE2MBY2ITFLM5QI8sCIaOUUVCPV2wqYnIhHgai91LCKT195Pie9m9EQze2vEXVHh4VVHoSplSSMiaiosaERkcg6cy8HDq45CXV6FLkHNsHFmJDydbKWORWQ22vo647vHesLVQYHT6SpMWn0EhaUaqWMREVkEFjQiMim/nb6K6euOo6xSi35tPPDN9O5Q2ltLHYvI7IT5OOP7x3rCzUGBM+lqPPTVURSUsKQRETU2FjQiMhkbj6fime9OolIrYlQHH6ya3BX2CiupYxGZrRBvJ/wwsyfcHW2QcFWNiV8dQT5LGhFRo2JBIyKTsPLARbz002noRGBi9wB8MjECCiv+EUbU2Fp7OeGHmT3g4WSDpMwiPPTVEeQVV0gdi4jIbPGnGyIyaqIo4r2dSXjntyQAwOP9g/HOPR0glwkSJyOyHK08q0fSPK+VtIlfHUEuSxoRUaNgQSMio6XViViw9Qw+33cRAPDS8FDMHxEGQWA5I2pqLT0c8cPMnvBytsG5rGJMXHkEOUUsaUREhsaCRkRG672dSfj2aCoEAXjnng54ckBLqSMRWbRgD0f8MDMS3s62OJ9djAdXRiNbXS51LCIis8KCRkRG6XxWEVYdvAQA+PD+cDzUI1DiREQEAC3cHfDDzJ7wUdriYk4JHvzqCLJY0oiIDIYFjYiMjiiKeHN7ArQ6EUPCvHBPhL/UkYjoP5q7O2DjzEj4udghOacED648gkwVSxoRkSGwoBGR0dmTlI2/z+fCWi5gwagwqeMQ0U0Eutnjh5k94edih0u5JXhwZTSuqsqkjkVEZPJY0IjIqGiqdHh7RyIAYFqfFmju7iBxIiK6lQDX6pLm38wOKXmleHDlEWQUsqQRETUECxoRGZV1h1NwKbcE7o42eGZgK6njENEdBLjaY+PjkQhwtcPlayUtnSWNiEhvLGhEZDRyiirwyV/nAQAvDg+Bk621xImIqC78XOywcWYkgtzskZpfigdWRCMtv1TqWEREJokFjYiMxtJdZ1FUUYUOfkqM78yNQYhMia+LHX6Y2RPN3exxpaAMD648wpJGRKQHFjQiMgpn0lXYeCINAPD62LaQyXgYNZGp8VHa4YeZkQh2d0B6YXVJS81jSSMiqg8WNCKSnCiKeOPXeIgiMDbcF12CXKWORER68lba4vuZPRHsUV3SHlgZjct5JVLHIiIyGSxoRCS57f9cxfGUAthay/DyiFCp4xBRA3k52+KHx3qipYcDrqrK8cCKI7iUy5JGRFQXLGhEJKkyjRaLf6veVv/J/q3g62IncSIiMgRPZ1v8MDMSrT0dkakux4Mro5GcUyx1LCIio8eCRkSSWnHgIjJU5fBzscPMfsFSxyEiA/JwssH3M3uijZcjstQVeHDlEVzIZkkjIrodFjQikkxGYRm+3H8RADB/ZCjsFHKJExGRobk72uD7x3oi1NsJ2UUVmPjVEVzILpI6FhGR0WJBIyLJvPt7Esordeje3BWjOvhIHYeIGombow2+u1bScooq8ODKozifxZJGRHQzLGhEJInjKfnYFpcBQQAWjmkLQeC2+kTmzNVBge8f64m2Ps7ILa6e7ng2kyWNiOj/saARUZPT6aq31QeAB7sFoL2fUuJERNQUmjko8N1jPdDO1xl5JRpM/OoIkjLVUsciIjIqLGhE1OQ2x1zBmXQ1nGys8NywEKnjEFETcrFX4LsZPdHBT4n8Eg0mrjyChAyWNCKiGixoRNSkisor8d4fSQCA2UNaw93RRuJERNTUlPbW2DCjB8L9lSgorcRDq44gPkMldSwiIqPAgkZETWr5ngvILdYg2N0BkyObSx2HiCSitLPG+uk90CnABYWllXjoq6M4k86SRkTEgkZETeZSbgnWHLoEAFgwOgwKK/4RRGTJqktad0QEukBVVomHvjqC01dY0ojIsvGnIyJqMot2JKBSK6J/Gw8MDPGUOg4RGQFnW2usn9YdXYKaQV1ehYdWHUFcWqHUsYiIJMOCRkRNYv+5HPyZmA0rmYDXRodxW30iquVka41107qjW/NmKCqvwsOrjuJUaoHUsYiIJMGCRkSNrlKrw1vbEwAAkyObo5Wnk8SJiMjYONpYYe2j3dG9uSuKKqowefUxxFxmSSMiy8OCRkSN7tsjl3EhuxiuDgrMHtxa6jhEZKQcbKzw9aPd0KNFdUmbsuYYYi7nSx2LiKhJsaARUaPKL9Hgw93nAADPDWsDpb21xImIyJjVlLTIYDcUXxtJO57CkkZEloMFjYga1bLd56Aur0KotxMe7BYodRwiMgH2CiusmdoNvVu5oUSjxZQ1x3A0OU/qWERETYIFjYgaTVKmGt8evQwAiBrTDnIZNwYhorqxU8ixeko39G3tjlKNFlO/Po4jLGlEZAFY0IioUYiiiDe2JUAnAiM7eCOypZvUkYjIxNhay/HV5K7o29odZZVaPPr1cRy+mCt1LCKiRsWCRkSN4o/4LEQn50FhJcP8EWFSxyEiE1VT0gaEeKCsUotpa4/j0AWWNCIyXyxoRGRw5ZVaLPqtelv9x/sFI8DVXuJERGTKbK3lWPFIFwwK9UR5pQ7T1h7H3+dzpI5FRNQoWNCIyOBWH7yEtPwyeDnb4In+LaWOQ0RmwMZKji8e7owhYZ6oqNJh+roT2H+OJY2IzA8LGhEZVJa6HJ/tvQAAeHlEKBxsrCRORETmwsZKjs8ndcHQtl7QVOnw2PoT2Hc2W+pYREQGxYJGRAa1ZGcSSjVaRAS6YFy4n9RxiMjMKKxk+OyhzrirXXVJm7k+BnuTWNKIyHywoBGRwcSmFWLLyXQA1dvqy7itPhE1AoWVDMsf6owR7b2h0erw+Dcx+CsxS+pYREQGwYJGRAah04l4fVs8AOC+zv7oFOAibSAiMmvWchk+mRiBUR18oNHq8MSGGOyKz5Q6FhFRg7GgEZFB/BKXjti0Qjgo5HhpeIjUcYjIAljLZfj4wU4Y3dEHlVoRT317EjvPsKQRkWljQSOiBiupqMK7vycBAJ4e1AqezrYSJyIiS2Ell+GjBzphbLgvqnQinvnuJH4/fVXqWEREemNBI6IG+2LfRWSpKxDoao9pvVtIHYeILIyVXIYP7w/H3Z2ulbTvT2HHPyxpRGSaWNCIqEHS8kux8u9kAMCro8Jgay2XOBERWSIruQxL7++EeyP8oNWJmPXDKfwalyF1LCKiemNBI6IGeee3RGiqdOjdyg3D2npJHYeILJhcJuD9CeEY38UfWp2I2T+cwi+x6VLHIiKqFxY0ItLb4Yu5+P1MJmQCsHB0OwgCt9UnImnJZQLeu68j7u/qD50IzN0Yi62nWNKIyHSwoBGRXqq0Orz5awIAYFKPIIR4O0mciIiomkwm4N17O+LBbgHQicC8H2Ox5eQVqWMREdUJCxoR6eWH42lIyiyC0s4a84a2kToOEdF1ZDIB79zTARO7B0InAs9tisPmGJY0IjJ+ZlfQFi1ahF69esHe3h4uLi43fB4XF4eJEyciICAAdnZ2CAsLw8cff3zDdRUVFXj11VcRFBQEGxsbNG/eHGvWrGmC74DI+KlKK7F011kAwNwhrdHMQSFxIiKiG8lkAhbd3R4P9wyEKAIvbI7Dj8fTpI5FRHRbVnW56MCBAwZ7YL9+/Qx2r5vRaDSYMGECIiMjsXr16hs+j4mJgaenJzZs2ICAgAAcPnwYM2fOhFwuxzPPPFN73f3334+srCysXr0arVq1wtWrV6HT6Ro1O5Gp+Piv8ygorURrT0dM6hkkdRwioluSyQS8Na49ZIKA9dGX8eJP/0Aniniwe6DU0YiIbkoQRVG800Uymcwgi/8FQUBVVVWD71MXa9euxZw5c1BYWHjHa59++mkkJiZiz549AICdO3fiwQcfRHJyMlxdXfV6vlqthlKphEqlgrOzs173IDJGF7KLMPyjv1GlE/HN9O7o29pD6khERHckiiLe+DUBaw+nAADeuacDHurBkkZETaM+3aBOI2iBgYG3LGg5OTkoLS2tvpmVFdzd3QEAubm5tWXMwcGh9n1jpFKpriti27ZtQ9euXfHee+/hm2++gYODA8aOHYu33noLdnZ2EiYlkpYoinhzeyKqdCKGhHmxnBGRyRAEAVFj2kImCFhz6BJe+fk0dKKIhzkLgIiMTJ3WoKWkpODSpUs3vGbNmoXKykqMHDkS+/fvR0lJCTIyMpCRkYGSkhLs378fo0ePhkajwezZs3Hp0qXG/n7q7fDhw9i4cSNmzpxZ+15ycjIOHjyIM2fO4Oeff8ZHH32EzZs346mnnrrlfSoqKqBWq697EZmbvWezceBcDqzlAhaMCpM6DhFRvQiCgNdGh2FGnxYAgAVbz2B9dIq0oYiI/o/em4Rs3boVzz//PGbMmIHt27ejb9++sLa2rv3c2toaffv2xbZt2zBjxgw899xz2LZtm17PevnllyEIwm1fSUlJ9b7vmTNnMG7cOERFRWHYsGG17+t0OgiCgG+//Rbdu3fHyJEj8eGHH2LdunUoKyu76b0WL14MpVJZ+woICNDreyUyVpoqHd7anggAmNanBZq7O0iciIio/gRBwKujwvB4v2AAwMJf4rkFPxEZlTqtQbuZfv36ITo6GtnZ2WjWrNltry0oKICHhwd69+6N/fv31/tZOTk5yMvLu+01wcHBUCj+3UnuTmvQEhISMHDgQMyYMQOLFi267rMpU6bg0KFDuHDhQu17iYmJaNu2Lc6dO4fWrVvfcL+KigpUVFTU/rNarUZAQADXoJHZ+OpAMhb9lgh3Rxvsfb4/nGyt7/xFRERGShRFLP49CSsPJMNBIcfvs/sh0M1e6lhEZKYMvgbtZv755x84OzvfsZwBQLNmzaBUKhEXF6fXszw8PODhYbi1LvHx8Rg0aBCmTJlyQzkDgN69e2PTpk0oLi6Go6MjAODcuXOQyWTw9/e/6T1tbGxgY2NjsIxExiSnqAKf/HUeAPDi8BCWMyIyeYIg4KXhoYhNLcSxlHzM+zEWGx+PhFzW8E3RiIgaQu8pjqIoQqVSISsr647XZmVl1Wk3RUNITU1FbGwsUlNTodVqERsbi9jYWBQXFwOontY4cOBADBs2DPPmzUNmZiYyMzORk5NTe4+HHnoIbm5uePTRR5GQkIADBw7ghRdewLRp07hJCFmkpbvOoqiiCh38lBjf+ea/pCAiMjVymYCl94fD0cYKJy4X4Mv9F6WORESkf0Hr1q0bRFHE7Nmzb3s+WM01oiiie/fu+j6uzhYuXIiIiAhERUWhuLgYERERiIiIwIkTJwAAmzdvRk5ODjZs2AAfH5/aV7du3Wrv4ejoiN27d6OwsBBdu3bFpEmTMGbMGHzyySeNnp/I2JxJV2HjieqDXaPGtIWMv10mIjMS4GqPqDFtAQDLdp/DmXSVxImIyNLpvQZtz549GDp0KACga9eumDdvHvr27QsfHx8AQGZmJg4cOIBly5bh+PHjEAQBf/75JwYMGGCw8MaM56CRORBFEQ+sOIJjKfkYG+6LTyZGSB2JiMjgRFHEkxtOYmd8Jlp5OmL7s31gay2XOhYRmZH6dAO9CxoArFq1Ck8//TQqKytveU6aKIqwtrbG559/junTp+v7KJPDgkbmYPs/GXjmu1OwtZZhz3MD4OvCKb5EZJ7ySzQYtuwAcosr8Gjv5oga007qSERkRurTDfSe4ggAM2bMQFxcHB5++GE4OTlBFMXrXk5OTnjkkUcQFxdnUeWMyByUabRY/Fv18RVP9m/FckZEZs3VQYH3x3cEAHx9KAUHz+dKnIiILFWDRtD+SxRFJCcnIze3+g80d3d3BAcH33JkzdxxBI1M3cd/nseyP8/Bz8UOf87rDzsFp/sQkflbsPU0NhxJhbezLXbO6QsXe8Wdv4iI6A6aZJv9/ycIAlq2bImWLVsa6pZEJJGMwjJ8sb/6HMD5I0NZzojIYrwyMgyHLuThUm4JXvslHp9y7S0RNbEGTXH8f1euXMGpU6dw6tQpXLlyxZC3JqIm9O7vSSiv1KF7c1eM6uAjdRwioiZjr7DCsgc6QS4T8GtcBn6JTZc6EhFZmAYXtMuXL+PJJ5+Eh4cHgoKC0LVrV3Tt2hVBQUHw9PTEU089hcuXLxsiKxE1geMp+dgWlwFBABaOaWux05SJyHJ1CnDBs4NaAQAWbD2DjMIyiRMRkSVpUEHbvn07OnTogJUrVyIvL++GTUJyc3OxYsUKdOjQAb/99puhMhNRI9HpRLzxazwA4MFuAWjvp5Q4ERGRNJ4Z2ArhAS4oKq/Ccz/GQaczyJJ9IqI70rugXbx4Effffz+Ki4sREBCAjz76CHFxcSgsLERhYSHi4uKwbNkyBAQEoLi4GOPHj8fFixcNmZ2IDGxzzBWcSVfDycYKzw0LkToOEZFkrOQyLLs/HHbWckQn52HNoUtSRyIiC6F3QXv33XdRXl6OoUOHIikpCbNmzUKHDh3g7OwMZ2dndOjQAbNnz0ZSUhIGDx6M8vJyLFmyxJDZiciAisor8d4f1dvqzx7SGu6ONhInIiKSVrCHI14dFQYAeO+PszibWSRxIiKyBHoXtD///BOCIODLL7+Era3tLa+ztbXFl19+CQDYvXu3vo8joka2fM8F5BZrEOzugMmRzaWOQ0RkFCb1CMTAEA9oqnSYszEWFVVaqSMRkZnTu6BdvXoVLi4uaNGixR2vbdmyJVxcXJCZmanv44ioEV3KLamdvrNgdBgUVgbd4JWIyGQJgoAl4zvC1UGBxKtqLNt9XupIRGTm9P4pzNHREcXFxSgvL7/jteXl5SguLoa9vb2+jyOiRrRoRyIqtSL6t/HAwBBPqeMQERkVTydbvHNPBwDAigMXcTQ5T+JERGTO9C5oERERqKqqqp2+eDsrVqxAVVUVunTpou/jiKiRHDiXgz8Ts2AlE/Da6DBuq09EdBPD23tjQhd/iCIw78c4FJVXSh2JiMyU3gVtxowZEEURL774It59912Uld14RkhhYSHefPNNvPDCCxAEAY899liDwhKRYVVqdXhrewIAYHJkc7TydJI4ERGR8Yoa2w4BrnZILyzD69sSpI5DRGZKEEVR74M9Jk2ahO+//x6CIMDBwQHdu3eHn58fKioqkJqaitOnT6O0tBSiKOKhhx7Chg0bDJndqKnVaiiVSqhUKjg7O0sdh+im1h66hNd/TYCrgwJ7nxsApb211JGIiIza8ZR83L8iGqIIfDGpM0Z08JE6EhGZgPp0A6uGPOibb75Bu3btsGTJEhQVFWHPnj03XOPk5ISXX34ZL730UkMeRUQGll+iwYe7zwEAnhvWhuWMiKgOujV3xRP9W+KLfRfxys+n0SWoGTydb72bNRFRfTVoBK1GSUkJdu3ahZMnTyI3NxcA4OHhgYiICAwbNgwODg4NDmpqOIJGxu61rWfwzZHLCPV2wo5ZfSGXce0ZEVFdaKp0uPuzQ0i4qsaAEA98PbUb1+8S0W3VpxsYpKDRjVjQyJglZaox8uO/oROB7x/riciWblJHIiIyKeeyijD604PQVOnw1t3t8UjPIKkjEZERq0834GFHRBZGFEW8sS0BOhEY2cGb5YyISA9tvJzw8vBQAMCiHQm4mFMscSIiMhcNWoNW4+jRo9i8eTNOnTqFnJwcAP9OcRw/fjx69OhhiMcQkQH8EZ+F6OQ8KKxkmD8iTOo4REQma2qv5vgrKQuHLuRh3sZYbH6yF6zl/N03ETVMg6Y45uXlYerUqfjtt98AVP9m/rqbX5uPPWrUKHz99ddwc7Oc39RziiMZo/JKLYYtO4DU/FI8M7AVnr8rROpIREQm7aqqDHctOwB1eRVmDW6NeUPbSB2JiIxQk+ziWFFRgaFDhyIuLg6iKKJTp04YOHAggoKq52BfvnwZe/fuRWxsLHbs2IFhw4YhOjoaCoVC30cSUQOtOXQJqfml8HK2wZMDWkodh4jI5Pko7fD2PR0w6/tT+GzvBQwI8UDnwGZSxyIiE6Z3Qfv0008RGxsLd3d3rFu3DiNGjLjpdb/99humTJmC2NhYLF++HPPmzdM7LBHpL0tdjuV7LgAAXh4RCgcbg8xwJiKyeGPDffFnQha2xWVg3sZY/Da7L+wV/DOWiPSj90TpjRs3QhAErF69+pblDABGjhyJVatWQRRFfP/99/o+joga6L2dZ1Gq0SIi0AXjwv2kjkNEZFbeGtcePkpbpOSV4u0diVLHISITpndBO3fuHGxtbTFmzJg7Xjt27FjY2dnh7Nmz+j6OiBogNq0QP528AgCIGtMOMp55RkRkUEp7a3wwIRwA8N3RVOxJypI4ERGZKr0LmlarhVwur9O1giBALpdDp9Pp+zgi0pNOJ+L1bfEAgPs6+6NTgIu0gYiIzFTvVu6Y3qcFAODFzaeRV1whcSIiMkV6F7QWLVqgpKQEhw8fvuO1hw8fRnFxMVq0aKHv44hIT7/EpSM2rRAOCjleGs5dG4mIGtMLd4WgjZcjcosrMH/L6Rt2uCYiuhO9C9q4ceMgiiIeffRRXLp06ZbXJScnY9q0aRAEAXfffbe+jyMiPZRUVOHd35MAAE8PagVPZ1uJExERmTdbazmWPdAJ1nIBuxKysCnmitSRiMjE6H0OmkqlQocOHXDlyhXY2dlh4sSJGDBgAPz8/FBRUYHU1FTs27cPmzdvRlVVFQICAvDPP/9AqVQa+nswSjwHjYzBB3+cxfK9FxDoao9dc/vB1rpu05KJiKhhvth3EUt2JsFBIcfvs/sh0M1e6khEJKH6dIMGHVR97tw53HvvvUhISKg9lPr/iaKIdu3aYcuWLWjdurW+jzI5LGgktbT8Ugz+cD80VTqseKQL7mrnLXUkIiKLodWJmLjyCI6l5KNrUDNsfDwScm7QRGSx6tMN9J7iCABt2rTBqVOnsHbtWowePRq+vr5QKBRQKBTw8/PD6NGjsW7dOpw8edKiyhmRMVj8eyI0VTr0buWGYW29pI5DRGRR5DIBS+8Ph6ONFU5cLsCX+y9KHYmITESDRtDo1jiCRlKKvpiHiV8dgUwAfpvdF6He/HeQiEgKm06k4YXN/8BKJmDr073R3s8ylnoQ0fWabASNiIyPVifijV+rt9Wf1COI5YyISELju/hjeDtvVOlEzNkYi/JKrdSRiMjIsaARmZkfjqciKbMISjtrzBvaRuo4REQWTRAEvHNvB7g72uBCdjGW7EySOhIRGTmrht4gPj4eP/30E+Lj41FYWIjKyspbXisIAv7666+GPpKIbkFVWokP/jgLAJg7pDWaOSgkTkRERK4OCrw/viMeXXscXx9KweBQL/Rp7S51LCIyUnoXNFEUMXv2bHz++ecQRbFOBzHeaqdHIjKMj/86j4LSSrT2dMSknkFSxyEiomsGhnri4Z6B2HAkFc9visPOOX3hYs9fohHRjfQuaJ988gmWL18OAAgPD8eYMWPg5+cHW1sehEskhQvZRVgfnQIAWDimLazlnMFMRGRMXhkZhkMX8nAptwSv/RKPTydGSB2JiIyQ3gVt9erVEAQB8+bNw/vvv2/ITERUT6Io4s3tiajSiRgS5oW+rT2kjkRERP/HXmGFZQ90wn1fHMavcRkYEuaJcZ38pI5FREZG71+xX7hwAYIgICoqypB5iEgPe89m48C5HFjLBSwYFSZ1HCIiuoVOAS54dlArAMCCrWeQUVgmcSIiMjZ6FzQnJyc4OzvD0dHRkHmIqJ40VTq8tT0RADCtTws0d3eQOBEREd3OMwNbITzABUXlVXjuxzjodDySloj+pXdB69u3L1QqFa5evWrIPERUT+ujU3AptwTujjZ4ZmArqeMQEdEdWMllWHZ/OOys5YhOzsOaQ5ekjkRERkTvgvbaa6/BxsYGL7/8siHzEFE95BZX4OM/zwMAXhweAidba4kTERFRXQR7OOLVa1PS3/vjLM5mFkmciIiMhd4FLTw8HD///DN+/fVX9O/fH7t27UJmZqYhsxHRHSzddRZFFVXo4KfE+M7+UschIqJ6mNQjEANDPKCp0mHOxlhUVGmljkRERkAQ63CAmVwuN8zDBAFVVVUGuZexU6vVUCqVUKlUcHZ2ljoOmaGkTDVGfPw3RBHY/EQkujZ3lToSERHVU3ZROYZ/9DfySzR4on9LvDwiVOpIRNQI6tMN6jSCVnMQdUNfOp3OIN8gEQHfHU2FKAIj2nuznBERmShPJ1u8c08HAMCKAxdxNDlP4kREJLU6nYN26RIXrxIZE02VDtviMgAAE7sHSpyGiIgaYnh7b0zo4o9NMVcw78c47JzTl2uKiSxYnQpaUFBQY+cgonrYezYbhaWV8HSyQe9W7lLHISKiBooa2w5HLuUhLb8Mr29LwNL7w6WOREQS0XuTECKSzpaTVwAA90T4QS4TJE5DREQN5WhjhQ/v7wRBAH46eQW/n+YxRkSWigWNyMQUlGiwJykbAHAvd24kIjIb3Zq74on+LQEAr/x8GtnqcokTEZEU6jTF8c033wQAuLu746mnnrruvfpauHChXl9HRNV+/ScDlVoR7f2cEeLtJHUcIiIyoLlD2mD/2RwkXFXjxZ/+wddTu0EQOFOCyJLUaZt9mUwGQRAQEhKChISE696rK1EUIQgCtFrLOOOD2+xTYxn32SHEpRVi4ei2mNanhdRxiIjIwM5lFWH0pwehqdLhrbvb45Ge3AuAyNTVpxvUaQRt8uTJEAQBPj4+N7xHRE3nQnYx4tIKIZcJGNvJV+o4RETUCNp4OeHl4aF4c3sCFu1IQK+Wbmjp4Sh1LCJqInUqaGvXrq3Te0TUuH4+Vb05yIA2HnB3tJE4DRERNZapvZrjr6QsHLqQh3kbY7H5yV6wlnPrACJLwP+nE5kInU7EzyfTAXBzECIicyeTCfhgQjicba0Qd0WFT/dckDoSETURFjQiE3HkUh4yVOVwsrXC4DBPqeMQEVEj81Ha4e17OgAAPtt7ASdTCyRORERNgQWNyERsuTZ6NrqjL2yt5RKnISKipjA23Bdjw32h1YmYtzEWpZoqqSMRUSOr0xq04OBggzxMEARcvHjRIPcisiSlmqraQ0vv6+wncRoiImpKb41rj+Mp+UjJK8XbOxLxzrVRNSIyT3UqaCkpKQZ5GHd9JNLPrvgslGi0CHKzR5egZlLHISKiJqS0t8YHE8IxadVRfHc0FUPCPDEo1EvqWETUSOpU0Pbu3dvYOYjoNn46Wb17470R/vxFBxGRBerdyh3T+7TA6oOX8OLm0/hjjgvcuJsvkVmqU0Hr379/Y+cgolvIVJXj4IVcAMA9EZzeSERkqV64KwQHzuXgfHYx5m85jRWPdOEv7YjMEDcJITJyW2PTIYpA9+auCHSzlzoOERFJxNZajo8e7ARruYBdCVnYFHNF6khE1AgMVtCysrJw4sQJHDhwwFC3JLJ4oijip2t/Ad/LzUGIiCxeO18l5g0NAQC8sS0eqXmlEiciIkNrcEH79ttv0b59e/j6+qJHjx4YNGjQdZ8XFhZi6NChGDJkCPLz8xv6OCKLEp+hxvnsYiisZBjZ0UfqOEREZARm9gtG9+auKNFoMe/HWGh1otSRiMiAGlTQ5syZg8mTJyMhIQEKhQKCIEAUr/9DwsXFBd7e3ti7dy82btzYoLBElqZmc5Bhbb3gbGstcRoiIjIGcpmApfeHw9HGCicuF+DL/TzCiMic6F3Qtm/fjk8++QTOzs748ccfUVxcDA8Pj5teO2XKFIiiiJ07d+odlMjSVGp12BabAQC4r7O/xGmIiMiYBLjaI2pMWwDAst3ncCZdJXEiIjIUvQva559/DkEQ8MEHH2D8+PGQy+W3vDYyMhKCICAuLk7fxxFZnAPncpBXooG7owJ9W7tLHYeIiIzM+C7+GN7OG1U6EXM2xqK8Uit1JCIyAL0L2vHjxwEAEydOvOO1Dg4OUCqVyMrK0vdxRBZny8l0AMC4Tn6wknPDVSIiup4gCHjn3g5wd7TBhexiLNmZJHUkIjIAvX/qU6vVcHZ2hr193bb91mq1tx1lI6J/qUorsTuh+hcanN5IRES34uqgwPvjOwIAvj6UgoPncyVOREQNpXdB8/DwgFqtRklJyR2vTUlJQVFREXx8uAsdUV1sP50BjVaHUG8ntPV1ljoOEREZsYGhnni4ZyAA4PlNcSgs1UiciIgaQu+CFhkZCQD45Zdf7njtsmXLIAgCBgwYoO/jiCxKzfRGjp4REVFdvDIyDC3cHZCpLsdrv8RLHYeIGkDvgvb0009DFEXMnz8f58+fv+k1Op0OixcvxqeffgpBEPDss8/qHZTIUqTkliDmcgFkAjCuk6/UcYiIyATYK6yw7IFOkMsE/BqXgV9i06WORER60rugDRgwAHPnzkVaWhq6dOmCiRMn1k53XLhwIaZOnYrAwEAsWLAAAPDaa6+hY8eOhklNZMa2nKr+S7Vvaw94OttKnIaIiExFpwAXPDuoFQBgwdYzyCgskzgREelDEP//ZOl6+vDDDxEVFXXdWrT/Hljt4OCAt99+G7Nnz25YUhOjVquhVCqhUqng7Mw1RFQ3Op2Ifu/vxZWCMnz8YCeM6+QndSQiIjIhVVod7vsyGnFphYgMdsO3M3pAJhOkjkVk8erTDRpc0ABApVJh8+bNiI6OxtWrV6HT6eDl5YWePXtiwoQJcHNza+gjTA4LGunj2KV83L8iGo42Vjj+6hDYKbjzKRER1U9yTjFGfXIQZZVaLBgVhhl9g6WORGTx6tMNrPR9SHJyMoKDq/8Pr1QqMX36dEyfPv22X/P999/X6dw0Iku15eQVAMDIDt4sZ0REpJdgD0e8OioMC7aewXt/nEXf1h4I8XaSOhYR1ZHea9AGDx6M9PS6L0BdvXo1Jk+erO/jiMxeeaUWO/65CgC4l7s3EhFRA0zqEYiBIR7QVOkwZ2MsKqq0UkciojrSu6BdvnwZgwcPRnZ29h2vXb58OWbOnAmdTqfv44jM3q6ELBRVVMG/mR26N3eVOg4REZkwQRCwZHxHuDookHhVjWW7b77jNhEZH70L2r333otz585h6NChKCgouOV17733Xu0GIcuXL9f3cURmr2Z6470RflzQTUREDebpZIt37ukAAFhx4CKOJudJnIiI6kLvgvb9999j+PDhOH36NO666y4UFRXdcE1UVBTmz58PQRCwZs0aPPnkkw0KS2SusovKceBcDgDgHk5vJCIiAxne3hsTuvhDFIF5P8ahqLxS6khEdAd6FzRra2ts2bIF/fv3x4kTJzBq1CiUlf173sbzzz+Pt99+G3K5HN999x2mTJlikMBE5mhbbAZ0ItA50AUt3B2kjkNERGYkamw7BLjaIb2wDK9vS5A6DhHdgd4FDQBsbW2xfft29OjRAwcPHsTdd9+N8vJyPPnkk/jwww9hbW2NzZs34/777zdUXiKz9NPJ6g13uDkIEREZmqONFT68vxMEAfjp5BX8fvqq1JGI6DYaVNCA6oOod+7cifDwcPz5559o2bIlVq5cCTs7O2zbtg1jx441RE4is5WQoUbiVTUUchlGd/SROg4REZmhbs1d8UT/lgCAV34+jWx1ucSJiOhWGlzQgOpz0Hbv3o3Q0FBcvXoVjo6O2LlzJ4YNG2aI2xOZtZ9PVW8OMjjMEy72ConTEBGRuZo7pA3a+jijoLQSL/70D0RRlDoSEd1EnQ6qfvPNN+t0sz59+iAxMRH9+vXD3r17sXfv3huuWbhwYf0SEpmxKq0OW2MzAHB6IxERNS6FlQwfPdgJoz89iH1nc7DhaCoe6RkkdSwi+j+CWIdfn8hkMghC3bb9FkXxptfWvK/VWsZBiWq1GkqlEiqVCs7OzlLHISO192w2Hv36OFwdFDgyfzAUVgYZ1CYiIrqlNQcv4c3tCbC1lmHHrL5o6eEodSQis1efblCnEbTJkyfXuaARUd1tubY5yNhwX5YzIiJqElN7NcdfSVk4dCEP8zbGYvOTvWAt599BRMaiTgVt7dq1jRyDyPKoyyuxKz4TAHAfpzcSEVETkckEfDAhHHctO4C4Kyp8uucC5g1tI3UsIrqGvy4hksjvp6+iokqH1p6OaO/HabBERNR0fJR2ePueDgCAz/ZewMnUAokTEVENFjQiifz37DNOISYioqY2NtwXY8N9odWJmLcxFqWaKqkjERFY0IgkkZZfimOX8iEIwN0RvlLHISIiC/XWuPbwUdoiJa8Ub+9IlDoOEaGOBU0ul0Mul6Ndu3Y3vFefl5VVnZa8EZm9n09Vj571bukOH6WdxGmIiMhSKe2t8cGEcADAd0dTsScpS+JERFSngiaKYu3rZu/V9aXT6RrtGyEyFaIoYsvJ6sOp7+3sJ3EaIiKydL1buWN6nxYAgBc3n0ZecYXEiYgsW52GtC5dugQAsLa2vuE9Iqqfk6mFSMkrhb1CjrvaeUsdh4iICC/cFYID53JwPrsY87ecxopHunB9NJFE6lTQgoJuPGX+Zu8R0Z39dG30bHh7bzjYcNovERFJz9Zajo8e7IS7PzuEXQlZ2BRzBfd3DZA6FpFF4iYhRE2ovFKL7XEZAHj2GRERGZd2vkrMGxoCAHhjWzxS80olTkRkmVjQiJrQnqRsqMur4Ku0RWSwm9RxiIiIrjOzXzC6N3dFiUaLeT/GQqsT7/xFRGRQdZpftX79eoM9cPLkyQa7F5Gpqdkc5O4IP8hknNtPRETGRS4TsPT+cIz4+G+cuFyAL/dfxNMDW0kdi8iiCOJ/t2a8BZlMZrCFolqt1iD3MXZqtRpKpRIqlQrOzs5SxyEjkFtcgZ7v/IUqnYg/5/VDK08nqSMRERHd1KYTaXhh8z+wkgnY+nRvtPdTSh2JyKTVpxvUaQStX79+3MmHqIF+jctAlU5EuL+S5YyIiIza+C7++CsxGzvjMzFnYyy2P9sHttZyqWMRWYQ6FbR9+/Y1cgwi87flZPXh1PdycxAiIjJygiDgnXs74MTlAlzILsaSnUmIGtNO6lhEFoGbhBA1gXNZRTidroKVTMCYcF+p4xAREd2Rq4MC74/vCAD4+lAKDp7PlTgRkWUwu4K2aNEi9OrVC/b29nBxcbnh87i4OEycOBEBAQGws7NDWFgYPv744+uumTp1KgRBuOHVrh1/c0T6qRk9GxjqCVcHhcRpiIiI6mZgqCce7hkIAHh+UxwKSzUSJyIyf2ZX0DQaDSZMmIAnn3zypp/HxMTA09MTGzZsQHx8PF599VXMnz8fy5cvr73m448/xtWrV2tfaWlpcHV1xYQJE5rq2yAzotWJ+PlU9e6N93X2kzgNERFR/bwyMgwt3B2QqS7Ha7/ESx2HyOzVaQ2aKXnjjTcAAGvXrr3p59OmTbvun4ODgxEdHY0tW7bgmWeeAQAolUoolf/uVrR161YUFBTg0UcfbZzQZNYOX8xFlroCSjtrDAz1lDoOERFRvdgrrLDsgU6474vD+DUuA0PCPDGuE3/hSNRYzG4ETR8qlQqurq63/Hz16tUYMmQIgoKCbnlNRUUF1Gr1dS8i4N/pjWPDfWFjxR2wiIjI9HQKcMGzg6rPQ1uw9QwyCsskTkRkviy+oB0+fBgbN27EzJkzb/p5RkYGfv/9d8yYMeO291m8eHHtyJtSqURAQEBjxCUTU1xRhZ1nMgEA93J6IxERmbBnBrZCeIALisqr8NyPcdDp7niULhHpwSQK2ssvv3zTTTv++0pKSqr3fc+cOYNx48YhKioKw4YNu+k169atg4uLC+6+++7b3mv+/PlQqVS1r7S0tHrnIfOz80wmyiq1CHZ3QKcAF6njEBER6c1KLsOy+8NhZy1HdHIe1hy6JHUkIrNkEmvQnnvuOUydOvW21wQHB9frngkJCRg8eDBmzpyJBQsW3PQaURSxZs0aPPLII1Aobr/zno2NDWxsbOqVgczflpPVm4Pc29mPh70TEZHJC/ZwxKujwrBg6xm898dZ9G3tgRBvJ6ljEZkVkyhoHh4e8PDwMNj94uPjMWjQIEyZMgWLFi265XX79+/HhQsXMH36dIM9myxHemEZopPzAAB3R3B6IxERmYdJPQLxV2IW9p7NwZyNsdj6dC+usSYyIJOY4lgfqampiI2NRWpqKrRaLWJjYxEbG4vi4mIA1dMaBw4ciGHDhmHevHnIzMxEZmYmcnJybrjX6tWr0aNHD7Rv376pvw0yA1tPpUMUgZ7BrvBvZi91HCIiIoMQBAFLxneEq4MCiVfVWLb7vNSRiMyK3iNo69evr9f1NjY2cHFxQWho6G13Q2yohQsXYt26dbX/HBERAQDYu3cvBgwYgM2bNyMnJwcbNmzAhg0baq8LCgpCSkpK7T+rVCr89NNPNxxiTVQXoij+Z3qjv8RpiIiIDMvTyRbv3NMBT2yIwYoDFzEwxAM9gt2kjkVkFgRRFPXagkcmk+m9pqZly5aYO3fuLQ+TNgdqtRpKpRIqlQrOzs5Sx6EmFptWiLs/OwRbaxmOvzoETrbWUkciIiIyuBc2xWFTzBX4udhh55y+/PuO6Bbq0w30nuLYr18/9OvXD87OzqjpeEFBQejRowd69OhRO0omiiKUSiX69u2L8PBw2NjY4MKFC3jmmWcwceJEfR9PZNRqRs/uaufNv6yIiMhsRY1thwBXO6QXluH1bQlSxyEyC3oXtH379qFjx45Qq9WYO3cuUlNTkZycjMOHD+Pw4cNITk5GWloa5s2bB5VKha5du+LkyZPIz8/H+++/D7lcjh9//BE//PCDIb8fIslpqnTYFpcBgNMbiYjIvDnaWOHD+ztBEICfTl7B76evSh2JyOTpXdBWr16N5cuXY9GiRVi6dCn8/G7cpc7X1xcffPAB3nnnHSxbtgzffPMNbG1t8dxzz+H111+HKIr4+uuvG/QNEBmbvWezUVhaCU8nG/Rp5S51HCIiokbVrbkrnujfEgDwys+nkVdcIXEiItOmd0H78ssvIZfLMXv27DteO2vWLMjlcixfvrz2vccffxyCICA2NlbfCERGqWZ64z0RfpDLePYZERGZv7lD2iDMxxkFpZX4cPc5qeMQmTS9C1pSUhIcHR1hZ2d3x2vt7Ozg6OiIxMTE2vfc3Nzg4uKCwsJCfSMQGZ2CEg32JGUD4PRGIiKyHAorGV4f0xYA8P2xVJzNLJI4EZHp0rugKRQKqFQqXL58+Y7XpqSkoLCwENbW/26WIIoiSkpK0KxZM30jEBmd7f9koFIrop2vM0K8naSOQ0RE1GR6BLthRHtv6ETgre0J0HOjcCKLp3dB69WrFwBg5syZKC8vv+V1FRUVtdMZe/fuXft+WloaNBrNTdeuEZmqn06mA+DoGRERWab5I8KgkMtw8EJu7YwSIqofvQtaVFQU5HI5/vzzT7Rt2xZLly5FdHQ0UlJSkJKSgujoaCxduhTt2rXDn3/+CblcjoULF9Z+/aZNmwAA/fv3b/h3QWQELuYUIzatEHKZgLHhvlLHISIianKBbvZ4tE9zAMCiHYmo1OqkDURkgqz0/cKuXbti06ZNmDJlClJSUvDiiy/e9DpRFOHk5IS1a9eia9eute87OjripZdewqRJk/SNQGRUajYH6d/GAx5ONhKnISIiksYzA1vhp5grSM4twTfRlzGtTwupIxGZFEFs4AThrKwsfPzxx9i2bRuSkpKg01X/pkQmkyE0NBRjx47FrFmz4O3tbZDApqI+p4WT6dPpRPRZsgcZqnIsfygCoztyBI2IiCzXd0dT8crPp6G0s8a+5wegmYNC6khEkqpPN2hwQfsvjUaDgoICAECzZs2gUFju/xlZ0CzL4Yu5eOiro3CytcLxV4fA1loudSQiIiLJaHUiRn3yN5IyizC1V3O8Prad1JGIJFWfbqD3GrSbUSgU8PLygpeXl0WXM7I8W65tDjK6oy/LGRERWTy5TMBro6u33f/myGVcyOa2+0R1pfcatP9XVFSEuLg45OTkAAA8PDwQHh4OJyduNU7mrVRThd9PXwUA3NeZu5ISEREBQO9W7hgS5oU/E7OwaEcivn60u9SRiExCg0fQjh07hhEjRqBZs2bo378/xo8fj/Hjx6N///5o1qwZRo4ciePHjxsiK5FR2hWfhRKNFoGu9ugSxHP9iIiIarwyMhRWMgF7z+Zg/7kcqeMQmYQGFbSVK1eid+/e2LVrF3Q6HURRhFKphFKphCiK0Ol02LlzJ3r16oWvvvrKUJmJjMpP13ZvvLezHwRBkDgNERGR8Qj2cMSUXs0BAG9vT0AVt90nuiO9C9rJkyfx1FNPQavVonv37ti6dStUKhXy8/ORn58PtVqNn3/+Gd27d4dWq8VTTz2FkydPGjI7keQyVeU4dCEXAHBvBA+nJiIi+n+zBrVGM3trnM8uxvfHUqWOQ2T09C5oH3zwAXQ6HR566CEcPnwYY8eOvW69maOjI8aNG4fo6GhMnDgRWq0WS5cuNUhoImOxNTYdOhHo1rwZAt3spY5DRERkdJT21pg7tA0A4MPd56Aqq5Q4EZFx07ugHThwADKZDEuXLr3ttC5BEPDhhx9CEATs379f38cRGR1RFPFTTM30Ro6eERER3cpD3QPR2tMRBaWV+PSv81LHITJqehe0nJwcKJVKeHl53fFaLy8vuLi4IDc3V9/HERmd+Aw1zmcXQ2Elw8gOPlLHISIiMlpWchleHRUGAFgXnYJLuSUSJyIyXnoXNBcXF6jVaqjV6jteW3OdUqnU93FERqdmc5Chbb2gtLOWOA0REZFxGxDiiQEhHqjUinjnt0Sp4xAZLb0LWo8ePaDT6bB48eI7XrtkyRJotVr07NlT38cRGZVKrQ7bYjMA8OwzIiKiulowKgxymYDdCVk4fIEzq4huRu+C9swzz0AURbz33nt44oknkJp64648Z8+exbRp0/Duu+9CEAQ8++yzDQpLZCwOnMtBXokG7o4K9GvtIXUcIiIik9DK0wkP9wgEALy5PQFanShxIiLjo3dBGzZsGF544QWIooivvvoKLVq0QKtWrdC/f3/07NkTvr6+aNu2LdatWwdRFPHiiy9iyJAhhsxOJJktJ9MBAOM6+cFK3uDz3omIiCzGnCFt4GxrhaTMIvx4Ik3qOERGp0E/WS5ZsgQbNmxA8+bNIYoikpOT8ffff+PYsWPIzMyEKIoIDg7Gt99+W6epkESmQFVaid2JWQCqD6cmIiKiumvmoMDsIdXb7i/ddRZF5dx2n+i/rBp6g4ceeggPPfQQTp06hZMnT9bu1Ojh4YGIiAhEREQ0OCSRMdlx+io0VTqEejuhrY+z1HGIiIhMziM9g/DtkctIzi3BZ3sv4uURoVJHIjIaDS5oNVjGyFLU7N54b2e/254BSERERDensJLhlZFhmLH+BNYcvIRJPQIR4GovdSwio8DFM0T1kJJbgpjLBZAJ1evPiIiISD+DwzzRp5U7NFodFv/ObfeJarCgEdXDllPVm4P0ae0BL2dbidMQERGZLkEQsGB0GGQC8NvpTBy7lC91JCKjUKeCJpfLDfKysjLYjEqiJqfTidhybXojzz4jIiJquFBvZzzYvWbb/XjouO0+Ud0KmiiKBnnpdLrG/n6IGs2JywW4UlAGRxsrDGvrLXUcIiIiszBvaBs42VjhTLq6dp03kSWr05DWpUuXGjsHkdGrGT0b2cEbdgq5xGmIiIjMg7ujDZ4Z1AqLf0/C+3+cxcgOPnCw4awrslx1+rc/KCiosXMQGbXySi12/HMVAHBvZ3+J0xAREZmXqb2b49ujqUjNL8WX+y/iuWEhUkcikgw3CSGqg90JWSiqqIKfix26N3eVOg4REZFZsbGS45WR1WehrTyQjPTCMokTEUmHBY2oDrb85+wzmYxnnxERERnaXe280aOFKyqqdFjye5LUcYgkw4JGdAfZReU4cD4XAHBPBHdvJCIiagyCIOC10W0hCMC2uAzEXC6QOhKRJFjQiO5gW2wGtDoREYEuCPZwlDoOERGR2Wrvp8SELtVrvd/ansBt98kisaAR3cFPJ6sPp+bmIERERI3v+WEhcFDIEZtWiG1xGVLHIWpyLGhEt5GQoUbiVTWs5QLGdPSROg4REZHZ83S2xVMDWwEAluxMQplGK3EioqbFgkZ0Gz+fqt4cZHCoF1zsFRKnISIisgzT+7SAn4sdrqrKsfJAstRxiJoUCxrRLVRpddgaWz214r4unN5IRETUVGyt5Xh5RPW2+1/uv4hMVbnEiYiaDgsa0S0cvJCLnKIKuDoo0L+Nh9RxiIiILMrojj7oEtQMZZVavPcHt90ny9HgglZYWIgPPvgAI0aMQPv27dGyZcvrPler1Vi/fj2++eYbiCJ34iHTseXa5iBjw32hsOLvMoiIiJqSIAhYOLotgOq/k/+5UihtIKImYtWQLz5w4AAmTJiA3Nzc2vIlCNcf4uvs7IyPP/4YsbGxcHd3x4gRIxrySKImUVReiT/iMwFUH05NRERETS88wAX3Rvhhy6l0vPlrAjY9EXnDz5pE5kbvYYHLly9j7NixyMnJwfDhw/HNN9+gWbNmN732iSeegCiK2Lp1q76PI2pSv52+iooqHVp5OqKDn1LqOERERBbrheEhsLOW48TlAuw4fVXqOESNTu+CtmTJEqjVakyePBk7duzApEmToFDcfJe7mlGzI0eO6Ps4oib179lnfvxNHRERkYR8lHZ4vH8wAGDxb0kor+S2+2Te9C5ou3btgiAIeOutt+54rb+/P+zs7JCSkqLv44iaTFp+KY5dyocgAHd34vRGIiIiqT3eryV8lLZILyzD6oOXpI5D1Kj0Lmjp6elwdHREQEBAna63t7dHeTm3SCXj9/Op6tGzXi3d4OtiJ3EaIiIislPI8eLwEADA53svILuIP1OS+dK7oNnZ2aGsrAw6ne6O15aUlKCgoOCWa9SIjIUoithysvpw6nsjePYZERGRsRgX7ofwABeUaLRY+sc5qeMQNRq9C1pYWBi0Wi1iY2PveO3PP/8MnU6Hzp076/s4oiZxMrUQKXmlsFfIMby9t9RxiIiI6BqZTMDC0WEAgB9j0hCfoZI4EVHj0LugTZgwAaIo4vXXX7/t+Wbnz5/H888/D0EQMHHiRH0fR9QkakbPhrf3hoNNg06hICIiIgPrEuSKMeG+EEXgre0JPGOXzJLeBe2pp55Cu3btsGPHDowaNQp//PFH7XTHS5cuYd++fXjppZfQtWtXZGdno0ePHnj44YcNFpzI0CqqtPg1LgMAcF9nTm8kIiIyRi8ND4GNlQxHkvOxKyFL6jhEBqf3EIFCocAff/yBsWPHYufOnfjjjz9qP2vVqlXtfxZFEd26dcPWrVu5XTkZtT2J2VCXV8FHaYuewW5SxyEiIqKb8G9mj8f6BmP53gt457dEDAjxgI2VXOpYRAaj9wgaAPj6+uLIkSNYsWIFIiMjYW1tDVEUIYoiZDIZunXrhs8//xwHDx6Ep6enoTITNYqfrk1vvDvCD3IZf5lARERkrJ4c0BIeTja4nFeKdYdTpI5DZFCCaMDJu1qtFvn5+dDpdHBzc4OVleWu4VGr1VAqlVCpVHB2dpY6Dt1BbnEFer7zF6p0InbP7YfWXk5SRyIiIqLb+PFEGl7c/A+cbKyw74UBcHO0kToS0S3Vpxs0aATt/8nlcnh4eMDLy8uiyxmZnl/jMlClE9HRX8lyRkREZALGd/ZHO19nFFVU4cPd3HafzIdBCxqRqdpysvpw6nsj/CROQkRERHVRve1+WwDA98dScTazSOJERIZRp2Gu9evXG+yBkydPNti9iAzhXFYRTqerYCUTMCbcV+o4REREVEc9gt0wor03fj+Tibd3JGD9tO7clI5MXp0K2tSpUw32LzsLGhmbmtGzASGenL9ORERkYuaPCMNfidn4+3wu9p7NxqBQL6kjETVInQpav379+NsIMktanYitp6oL2vgunN5IRERkagLd7PFon+ZYsT8Zb29PRN/WHrCWcxUPma46FbR9+/Y1cgwiaURfzEOmuhxKO2sMDOVREERERKbomYGt8FPMFSTnluCb6MuY1qeF1JGI9MZfL5BF23Lt7LMx4T485JKIiMhEOdlaY97QEADAx3+dR0GJRuJERPpjQSOLVVxRhd/PZAIA7u3sL3EaIiIiaogHugUg1NsJqrJKfPzXeanjEOmNBY0s1s4zmSir1KKFuwMiAlykjkNEREQNIJcJeO3atvvfHLmMC9ncdp9MU53WoA0aNAgAEBQUhK+//vq69+pDEAT89ddf9f46osZQM73x3gg/boJDRERkBnq3cseQMC/8mZiFRTsS8fWj3aWORFRv9dokJDQ09Ib36oM/BJOxSC8sQ3RyHgDgbh5OTUREZDZeHRWG/eeysfdsDvafy0H/Nh5SRyKqlzoVtJpRM6VSecN7RKZo66l0iCLQo4UrAlztpY5DREREBtLC3QGTI5tj9cFLeHt7AnrP7gsrbrtPJqROBW3KlCl1eo/IFIiiWDu98T5uDkJERGR2Zg1qjS0nr+B8djG+P5aKRyKbSx2JqM7q9OuEQYMGYcKECde9l5qaivT09EYJRdSY/rmiwsWcEthayzCig7fUcYiIiMjAlPbWmDu0DQDgw93noCqrlDgRUd3VqaDt27cPhw4duu695s2bo3t3Lrwk01MzenZXO2842VpLnIaIiIgaw0PdA9Ha0xEFpZX4lNvukwmpU0GzsrKCRnPjgX+iKBo8EFFj0lTpsC0uAwDPPiMiIjJnVnIZXh0VBgBYF52CS7klEiciqps6FTRvb28UFBQgOTm5sfMQNaq9Z7NRUFoJTycb9G7pJnUcIiIiakQDQjwxIMQDlVoR7/yWKHUcojqp0yYhw4YNw5o1a9CjRw8MHDgQjo6OAACVSoVp06bV+WGCIGD16tX6JSUygJrpjXdH+HFHJyIiIguwYFQY/j6fi90JWTh8IRe9WrlLHYnotgSxDvMUs7KyMHDgQCQlJTXsYYIArVbboHuYCrVaDaVSCZVKBWdnZ6njEICCEg26v/MnKrUids7pi1Bv/u9CRERkCaJ+OYN10ZcR6u2EHbP6Qi7j2bzUtOrTDeo0gubl5YXTp0/jjz/+QHx8PMrKyvD666/D0dERzz33nEFCEzW27f9koFIroq2PM8sZERGRBZkzpA1+PpWOpMwibDqRhge7B0odieiW6jSCdjMymQze3t7IyMgwdCazwBE043P3Z4cQm1aIBaPCMKNvsNRxiIiIqAmtPngJb21PgLujAnufH8CdnKlJ1acb6L0IJyoqiqNnZDIu5hQjNq0QcpmAsZ18pY5DRERETeyRnkEIdndAbrEGn+29KHUcoltiQSOL8PPJ6kPV+7V2h6eTrcRpiIiIqKkprGR4ZWT1tvtrDl5CWn6pxImIbq5Oa9DuJD09HVu3bsWpU6eQk5MDAPDw8EBERATuuece+PpyxIKko9OJ+PlUdUG7rwvPPiMiIrJUg8M80aeVOw5eyMXi3xPx+aQuUkciuoHea9AAoLy8HC+88AJWrFhRuztjze0EoXp3HLlcjieeeALvvfcebG0tZ+SCa9CMx+GLuXjoq6NwsrXC8VeHwNZaLnUkIiIikkhSphojP/4bOhH48fFIdG/hKnUksgAG38XxZnQ6HcaNG4c///wToijCy8sLvXr1QlBQEADg8uXLOHz4MLKysvDZZ5/h3Llz+P3332uLG1FT2XJteuPojj4sZ0RERBYu1NsZD3YPxHdHU/HW9gT88nRvyLjtPhkRvQvamjVrsHv3btja2mLp0qWYPn06FArFdddoNBqsWrUKzz//PHbv3o01a9Zg+vTpDQ5NVFelmir8fvoqAODezpzeSERERMC8oW3wa2wGTqersOVUOsZzCQQZEb03CVm3bh0EQcAXX3yBJ5988oZyBgAKhQJPPfUUPvvsM4iiiLVr1zYkK1G97YrPQolGiwBXO3QNaiZ1HCIiIjIC7o42eGZQKwDAezuTUFJRJXEion/pXdDi4+OhUCgwadKkO177yCOPQKFQ4MyZM/o+jkgvP528AgC4N8Kf02uJiIio1tTezRHoao/sogp8uZ/b7pPx0LuglZeXw9bWFlZWd54laWVlBTs7O1RUVOj7OKJ6y1SV49CFXADAvZ39JE5DRERExsTGSo5XRoYCAFYeSEZ6YZnEiYiq6V3Q/P39oVarER8ff8drz5w5A5VKBX9/zu+lpvNLbDp0ItA1qBmC3BykjkNERERG5q523ujRwhUVVTos+T1J6jhEABpQ0EaMGAFRFDF9+nSoVKpbXqdWq/HYY49BEASMHDlS38cR1Ysoiv9Ob+TmIERERHQTgiDgtdFtIQjAtrgMxFwukDoSkf4F7eWXX4aLiwuOHz+O0NBQvP322zh48CAuXbqEpKQk7Nq1C6+88gpatGiBo0ePQqlU4qWXXjJkdqJbis9Q41xWMRRWMozq6CN1HCIiIjJS7f2UmHBtF8e3tidAp9P7iGAig9B7m30fHx/s2LED99xzD7KyshAVFXXT62rOSPv555/h48MflKlp1IyeDW3rBaWdtcRpiIiIyJg9PywEO/65iti0Qvz6TwbGdeLadZKO3iNoABAZGYnExERERUWhffv2EAQBoihCFEUIgoD27dvjjTfeQEJCAnr27GmozES3VanVYVtsBgDgPm4OQkRERHfg6WyLpwZWb7v/7u9JKNNoJU5ElkwQRVGvcVy1Wg0AcHBwgFwuBwBUVlYiPz8fAODq6gpra8sduVCr1VAqlVCpVHB2dpY6jkX5KzEL09edgLujAtHzB8Na3qDfQxAREZEFKK/UYvDS/UgvLMO8oW0wa3BrqSORGalPN9D7J1cXFxe4uroiIyOj9j1ra2t4eXnBy8vLossZSWtPUjYAYGQHH5YzIiIiqhNbazleHlG97f4X+y4iU1UucSKyVHr/9Oro6AhnZ2cEBAQYMg9Rg0Un5wEA+rRylzgJERERmZLRHX3QJagZyiq1eO8PbrtP0tC7oLVu3RolJSXQaDSGzEPUIFnqciTnlEAQgB4t3KSOQ0RERCZEEAQsHN0WALDlZDr+uVIobSCySHoXtEceeQSVlZXYsGGDIfMQNciRa6Nn7XydobTnNFsiIiKqn/AAF9wbUb3J2Ju/JkDP7RqI9KZ3QZs1axZGjRqFZ599FmvXroVOpzNkLiK9RF+sLmiRwRw9IyIiIv28MDwEdtZynLhcgN9OZ0odhyyM3uegzZgxA25ubpDL5Zg+fTpefPFFdO3aFR4eHrW7Ov4/QRCwevVqvcMS3UnN+rOeLGhERESkJx+lHR7vH4yP/jyPxb8nYnCYJ2ytb/7zLZGh6b3Nvkwmqz33rM4PEwRotZZxrgS32W96GYVl6PXuHsgEIDZqGJxtOcWRiIiI9FOm0WLQ0n24qirHi8ND8NSAVlJHIhNWn26g9whaVFSUvl9K1Chqpjd28FOynBEREVGD2CnkeHF4COZujMNney5gfBd/eDrZSh2LLAALGpmNmg1Cerbk9EYiIiJquHHhflh7+DLi0gqx9I9zWDK+o9SRyALwFF8yGzXrz7hBCBERERmCTPbvtvs/xqQhPkMlcSKyBAYtaKIooqCgAAUFBZJtSbpo0SL06tUL9vb2cHFxueHzuLg4TJw4EQEBAbCzs0NYWBg+/vjjG6779ttvER4eDnt7e/j4+GDatGnIy8trgu+A9JGWX4orBWWwkgno1txV6jhERERkJroENcOYcF+IIvDWdm67T42vwQVNrVbj3XffRbdu3WBrawt3d3e4u7vDzs4O3bp1w3vvvQe1Wm2IrHWi0WgwYcIEPPnkkzf9PCYmBp6entiwYQPi4+Px6quvYv78+Vi+fHntNYcOHcLkyZMxffp0xMfHY9OmTTh27Bgee+yxpvo2qJ5qRs86+ivhYKP3zF0iIiKiG7w0PAQ2VjIcSc7HroQsqeOQmdN7F0cA+Pvvv/HAAw8gKyvrlr9NEAQB3t7e+OGHH9C3b1+9g9bX2rVrMWfOHBQWFt7x2qeffhqJiYnYs2cPAOCDDz7AF198gYsXL9Ze8+mnn2LJkiW4cuVKnZ7PXRyb1ryNsdhyKh1PD2yJF+4KlToOERERmZkP/jiL5XsvIMjNHrvm9oONFbfdp7qrTzfQewQtKSkJw4cPR2ZmJjw9PREVFYU9e/YgKSkJSUlJ2LNnD6KiouDl5YWrV69ixIgROHv2rL6Pa1QqlQqurv9Oi4uMjERaWhp+++03iKKIrKwsbN68GSNHjrzlPSoqKqBWq697UdMQRZHnnxEREVGjenJAS3g42eByXinWH74sdRwyY3oXtKioKJSVlSEyMhJJSUmIiorCgAED0KZNG7Rp0wYDBgxAVFQUkpKSEBkZidLSUqPc+fHw4cPYuHEjZs6cWfte79698e233+KBBx6AQqGAt7c3lEolPvvss1veZ/HixVAqlbWvgICApohPAC7nleKqqhzWcgFdg7j+jIiIiAzPwcYKL9wVAgD45K/zyCuukDgRmSu9C9revXshCAJWr14NpVJ5y+ucnZ2xatUqAKidQlhfL7/8MgRBuO0rKSmp3vc9c+YMxo0bh6ioKAwbNqz2/YSEBMyePRsLFy5ETEwMdu7ciZSUFDzxxBO3vNf8+fOhUqlqX2lpaXp9r1R/NdvrdwpwgZ2C0w2IiIiocYzv7I92vs4oqqjCh7vPSR2HzJTeuymUlJRAqVQiNPTO633CwsLg4uKC0tJSvZ713HPPYerUqbe9Jjg4uF73TEhIwODBgzFz5kwsWLDgus8WL16M3r1744UXXgAAdOzYEQ4ODujbty/efvtt+Pj43HA/Gxsb2NjY1CsDGQa31yciIqKmULPt/gMrj+D7Y6mYHNkcId5OUsciM6N3QQsODsb58+eh0WigUChue61Go0FJSUmdytzNeHh4wMPDQ6+vvZn4+HgMGjQIU6ZMwaJFi274vLS0FFZW1/9XI5dXj8xwa1XjIooioi/ygGoiIiJqGj2C3TCivTd+P5OJt3ckYP207hAEQepYZEb0nuI4depUaDSa2umLt7Nq1SpUVlZiypQp+j6uzlJTUxEbG4vU1FRotVrExsYiNjYWxcXFAKqnNQ4cOBDDhg3DvHnzkJmZiczMTOTk5NTeY8yYMdiyZQu++OILJCcn49ChQ5g1axa6d+8OX1/fRv8eqO6Sc0uQXVQBhZUMnQObSR2HiIiILMD8EWFQyGX4+3wu9p7NljoOmRm9C9rcuXMxbtw4zJ07F++//z7Ky8tvuKa8vBxLly7F3Llzcffdd2Pu3LkNClsXCxcuREREBKKiolBcXIyIiAhERETgxIkTAIDNmzcjJycHGzZsgI+PT+2rW7dutfeYOnUqPvzwQyxfvhzt27fHhAkTEBISgi1btjR6fqqfmtGzzoEusLXm+jMiIiJqfIFu9ni0T3MAwNs7ElGp1UkbiMyK3uegTZs2DaIoYuvWrVCr1bC3t0e3bt1qR5gyMjJw4sSJ2rVq48aNu+nwb81GI+aG56A1jae/O4kd/1zFnCGtMWdIG6njEBERkYUoKq/EwA/2IbdYg6gxbfFo7xZSRyIjVp9uoHdBk8lkEAShwWuyBEGAVqtt0D2MEQta4xNFEd0W/YncYg02zuyJHtwkhIiIiJrQd0dT8crPp6G0s8b+FwbAxf72+zKQ5apPN9B7kxBjPNOMLMv57GLkFmtgYyVDp0AXqeMQERGRhXmgWwDWR6cgKbMIH/15Hq+PbSd1JDIDLGhksmrOP+vavBlsrLj+jIiIiJqW/Nq2+w+tOopvjlzGwz0D0cqT2+5Tw+i9SQiR1Go2COH5Z0RERCSVXq3cMSTMC1qdiEU7EqWOQ2aABY1Mkk4n1o6gRfL8MyIiIpLQq6PCYC0XsPdsDvafy7nzFxDdBgsamaSzWUUoKK2EvUKOjv4uUschIiIiC9bC3QGTI5sDAN7enoAqbrtPDcCCRiapZnpj1+ausJbzX2MiIiKS1qxBrdHM3hrns4vx/fE0qeOQCeNPtmSSoq9Nb+wZ7CpxEiIiIiJAaW+NeUOrz2T9cNdZqMoqJU5EpooFjUyOVifiaDI3CCEiIiLjMrF7IFp7OqKgtBLL95yXOg6ZKBY0MjmJV9VQl1fB0cYKHfyUUschIiIiAgBYyWVYMLotAGDt4RRcyi2ROBGZIhY0Mjk1uzd2a94MVlx/RkREREakfxsPDAjxQKVWxDu/cdt9qj/+dEsmp/b8M26vT0REREZowagwyGUCdidk4fCFXKnjkIlpUEHTaDSoqqq66WdfffUVHn74YYwfPx6rVq2CKIoNeRQRAKBKq8OxS/kAgMhgd4nTEBEREd2olacTHu4RCAB4c3sCtDr+HEx1p3dBW7lyJezs7DB16tQbPhs3bhyeeOIJfP/999iyZQsef/xx3H333Q2ISVQtPkONoooqONtaoa2vs9RxiIiIiG5qzpA2cLa1QlJmETad4Lb7VHd6F7TffvsNADB58uTr3t+xYwd+/fVXCIKASZMm4bHHHoNCocD27duxYcOGhqUli1ezvX73Fm6QywSJ0xARERHdXDMHBeYMqd52/4NdZ1FUzm33qW70Lmjx8fEAgO7du1/3/vr16yEIAhYsWID169djxYoV+PzzzyGKItavX9+wtGTxataf8fwzIiIiMnaPRAYh2N0BucUafL7votRxyEToXdCys7Ph4OAAFxeX697/66+/AACPPfZY7XsPPfQQBEFAbGysvo8jQqVWh+Mp19afcYMQIiIiMnLWchleHRUGAFj99yWk5ZdKnIhMgd4FraKi4oaNP86ePYv8/Hy0adMGfn5+te/b2NigWbNmUKlU+icli3c6XYVSjRYu9tYI8+b6MyIiIjJ+g0I90aeVOzRaHRb/zm336c70Lmje3t4oLS1Fenp67Xu///47AKBv3743XF9aWopmzZrp+zii2umNPVq4Qsb1Z0RERGQCBEHAgtFhkAnAb6cza3ejJroVvQta7969AQBvvPEGRFFEbm4uli9fDkEQMHLkyOuuvXjxIsrLy68bVSOqr5oDqiODOb2RiIiITEeotzMe7F697f5b2xOg47b7dBt6F7Tnn38ecrkcq1evhlKpREBAAJKTkxESEoIxY8Zcd23NyNr/byhCVFeaKh1OpBQAACJb8vwzIiIiMi3zhraBk40VTqersOVU+p2/gCyW3gUtIiICW7ZsQWBgIIqLi6HRaNC/f3/8+uuvkMvl1127YsUKAMCwYcMalpYsVtyVQpRVauHmoEAbL0ep4xARERHVi7ujDZ4d3AoA8N7OJJRUVEmciIyVVUO+ePTo0Rg9ejRycnLg6OgIOzu7G66pqqqqPf8sLCysIY8jC/bv9vpuEASuPyMiIiLTM6VXc3x7NBWX80qxYv9FzBsWInUkMkJ6j6D9l4eHx03LGQBYWVkhPDwc4eHhUCgUhngcWSCef0ZERESmzsZKjvkjqgcsVhxIRnphmcSJyBgZpKABQFZWFk6cOIEDBw4Y6pZEAIDySi1iUmvWn3GDECIiIjJdd7XzQo8Wrqio0uG9nUlSxyEj1OCC9u2336J9+/bw9fVFjx49MGjQoOs+LywsxNChQzFkyBDk53NbUaq/2LRCaKp08HCyQUsPrj8jIiIi0yUIAl4b3RaCAPwSm4GYywVSRyIj06CCNmfOHEyePBkJCQlQKBQQBOGGw6tdXFzg7e2NvXv3YuPGjQ0KS5aJ68+IiIjInLT3U2JCF38A3HafbqR3Qdu+fTs++eQTODs748cff0RxcTE8PDxueu2UKVMgiiJ27typd1CyXNE8/4yIiIjMzPPDQuCgkCM2rRC//pMhdRwyInoXtM8//xyCIOCDDz7A+PHjb9ha/78iIyMhCALi4uL0fRxZqPJKLWJTCwFw/RkRERGZD09nWzw1sHrb/Xd/T0KZRitxIjIWehe048ePAwAmTpx4x2sdHBygVCqRlZWl7+PIQsVcLoBGq4O3sy2au9lLHYeIiIjIYKb3aQE/FztcVZXjq7+TpY5DRkLvgqZWq+Hs7Ax7+7r90KzVam87ykZ0M//dXp/rz4iIiMic2FrLMX9kKADgi30XkakqlzgRGQO9C5qHhwfUajVKSkrueG1KSgqKiorg4+Oj7+PIQtWuP+P0RiIiIjJDozr4oGtQM5RVavH+H2eljkNGQO+CFhkZCQD45Zdf7njtsmXLIAgCBgwYoO/jyAKVVFQhLq0QABAZ7C5tGCIiIqJGULPtPgD8dPIK/rlSKG0gkpzeBe3pp5+GKIqYP38+zp8/f9NrdDodFi9ejE8//RSCIODZZ5/VOyhZnpjLBajSifBzsUOAq53UcYiIiIgaRXiAC+6N8AMAvPlrwg3HVpFl0bugDRgwAHPnzkVaWhq6dOmCiRMn1k53XLhwIaZOnYrAwEAsWLAAAPDaa6+hY8eOhklNFqFmeiPPPyMiIiJz98LwENhZy3HicgF+O50pdRySUIMOql66dCk++OADiKKIjRs3ori4GKIoYtGiRVi/fj0yMjJgb2+PZcuWISoqylCZyULUbBDC9WdERERk7nyUdniif0sAwOLfE1FeyW33LZVVQ28wb948TJ8+HZs3b0Z0dDSuXr0KnU4HLy8v9OzZExMmTICbG3/ApvoprqjC6XQVABY0IiIisgwz+wXjh+OpuFJQhjWHLuGpAa2kjkQSEEROcm0UarUaSqUSKpUKzs7OUscxOXuTsvHo2uMIdLXHgRcHSh2HiIiIqElsPZWOORtj4aCQ4++XBsHVQSF1JDKA+nSDBk1xJGos/64/c5U4CREREVHTGRvui3a+zijRaLGKh1dbJBY0Mkpcf0ZERESWSCYTMGdIGwDAusMpyC/RSJyImlqDCppGo8Hy5csxaNAgeHl5wcbGBnK5/JYvK6sGL3kjC6Aqq0R8xrX1Zzz/jIiIiCzMkDBPtPerHkX7iqNoFkfvxpSTk4PBgwcjPj6+zmc1cLkb1cXxS/nQiUALdwd4K22ljkNERETUpARBwJzBbTBj/QmsO5yCGX1awM3RRupY1ET0LmgvvfQSzpw5A2dnZ7zwwgsYPHgwPD09IZfLDZmPLNB/zz8jIiIiskSDwzzRwU+J0+kqfPX3Jbw8IlTqSNRE9C5o27dvhyAI+OGHHzB8+HBDZiILx/VnREREZOkEQcCcIa0xfd0JrI9OwWN9OYpmKfReg1ZaWgo7OzuWMzKowlINEjPVALiDIxEREVm2QaGe6OivRKlGi5Vci2Yx9C5orVu3hk6ng1bLU87JcI4k50MUgVaejvB04vozIiIislw1o2gAsP7wZeQVV0iciJqC3gVtxowZKC8vx5YtWwyZhyzcEZ5/RkRERFRrYIgnwv2VKKvUYuUBjqJZAr0L2lNPPYX77rsPM2fOxA8//GDITGTBatefcXt9IiIiomujaNXnoq2PvoxcjqKZPb03CREEAZs2bcJrr72GSZMm4eWXX0bbtm3h7e19269ZvXq1vo8kM5dXXIGzWUUAOIJGREREVGNAiAfCA1wQl1aIlQeS8crIMKkjUSNq0MnRH3zwAZYtWwZRFJGamorU1NTbXs+CRrdz9FI+ACDEy4m7FBERERFdU7MW7dGvj2N9dApm9guGO39WMlt6F7R169bhxRdfBAC0adMGAwYM4Dlo1CDcXp+IiIjo5ga08UCnABfEphVixf6LeHVUW6kjUSPRu6B9+OGHEAQBzz77LD766CMDRiJLxQOqiYiIiG6uZhRt6tfH8c2Ry5jZryU8nDiKZo703iTkwoULEAQBixYtMmQeslDZReW4kF0MQeD6MyIiIqKb6X9tFK28UocV+y9KHYcaid4FzdXVFc7OznBwcDBkHrJQR5Kr15+FejvDxV4hcRoiIiIi4yMIAuYOrd7RccPRy8guKpc4ETUGvQva8OHDoVKpcO7cOUPmIQv17/b6nN5IREREdCv9WrsjIrBmFI3nopkjvQvaG2+8AU9PT8ycORPFxcWGzEQWqOaAam4QQkRERHRr/z0XbcMRjqKZI703Cblw4QIWL16MuXPnokWLFnjiiSfQvn17+Pj43Pbr+vXrp+8jyUxlqspxKbcEMgHo3oLrz4iIiIhup19rd3QOdMHJ1EKs2J+M10ZzR0dzondBGzBgAARBAACIooh33nnnjl8jCAKqqqr0fSSZqZrRs3a+SijtrCVOQ0RERGTcakbRJq85hg1HLuPxfsHwdLaVOhYZiN4FLTAwsLagETUEzz8jIiIiqp++rd3RJagZYi4X4Mv9yVg4hqNo5kLvgpaSkmLAGGTJas4/4wYhRERERHVTcy7aI6uP4dujl/FEf46imQu9NwkhMoT0wjKk5pdCLhPQtXkzqeMQERERmYw+rdzRNagZKqp0+ILnopkNFjSSVM30xvZ+SjjZcv0ZERERUV39d0fHb4+mIkvNHR3NAQsaSYrnnxERERHpr3crN3Rr3gyaKh2+2MdRNHNQpzVogwYNAgAEBQXh66+/vu69+hAEAX/99Ve9v47MF88/IyIiItJfzSjapFVH8d2xVDzRvyW8lVyLZsrqVND27dsHAAgNDb3hvfrgro/0X2n5pUgvLIOVTEDXIK4/IyIiItJHr5bVo2jHUwrw5f6LeH1sO6kjUQPUqaDVjJoplcob3iPSV830xvAAFzjY6L2hKBEREZFFEwQBc4e0wUMcRTMLdfqpeMqUKXV6j6g+uL0+ERERkWFEtnRD9+auOJaSjy/2XcAb49pLHYn0xE1CSBKiKPKAaiIiIiIDEQQBc4a2BgB8fywNmSru6Giq9C5ogwYNwoQJE+p8/cSJEzF48GB9H0dmJiWvFJnqcijkMnQO5PozIiIiooaKDHZD9xau0Gh1+HzfBanjkJ70Lmj79u3DoUOH6nz9kSNH9NpYhMxTzehZpwAX2CnkEqchIiIiMn01a9EA4IdjabiqKpM4EemjyaY4arVa7uJItWrWn/Xk9EYiIiIig4ls6YYeNaNoe3kumilqkoJWUVGB7OxsODs7N8XjyMiJovjv+WfcIISIiIjIoOZcG0XbeDwNGYUcRTM1dd7bPDU1FSkpKde9p9Fo8Pfff0MUxZt+jSiKKCwsxPfffw+NRoNevXo1KCyZh4s5JcgpqoDCSoaIQBep4xARERGZlciWbugZ7Iojyfn4fN8FvH13B6kjUT3UuaB9/fXXePPNN697r6CgAAMGDLjj19YUuDlz5tQrHJmnmumNXQKbwdaa68+IiIiIDG3OkDZ4cOURbDyehqcGtIKvi53UkaiO6lzQXFxcEBgYWPvPly9fhkwmg7+//y2/RiaTwdnZGe3atcP06dMxcODAhqUls3CE2+sTERERNaqewW6IDHZDdHIePtt7AYvu4SiaqRDEW81PvAOZTAZvb29kZGQYOpNZUKvVUCqVUKlUXHv3H6IoouvbfyKvRINNT0SiW3NXqSMRERERmaWjyXl4YOURWMsF7HthIPw4iiaZ+nQDvTcJ+frrr/HRRx/p++Vkoc5lFSOvRANbaxnC/V2kjkNERERktnoEu6FXSzdUakV8vpfnopkKvQvalClTcP/99xsyC1mA6Iu5AICuQa5QWDXZKQ9EREREFqlmR8cfT6ThSkGpxGmoLvgTMjWpI8n5ALj+jIiIiKgpdG/hit6tro2i7eO5aKaABY2ajE4n4silawdU8/wzIiIioiZRM4q2iaNoJoEFjZpMUmYRCksrYa+Qo6O/Uuo4RERERBahW3NX9GnljkqtiM/2chTN2LGgUZOpOf+sW3NXWMv5rx4RERFRU5kzpDWA6lG0tHyOohkz/pRMTSaa558RERERSaJrc1f0be2OKp2Iz/dxR0djxoJGTUKrE3H02vqzSK4/IyIiImpyswfXjKJd4SiaEWNBoyaRkKFGUXkVHG2s0M6XB3cTERERNbX/jqJ9xnPRjBYLGjWJ6OTq88+6t3CFFdefEREREUmiZi3a5hiOohkrvX9SLiwsRF5eXp2vT09PR2pqqr6PIxNXe/4ZpzcSERERSaZL0L+jaMv3cBTNGNW7oH322Wdo2bIl3Nzc4OnpCV9fX7zyyitQqVS3/bquXbsiODhY76Bkuqq0Ohy7xAOqiYiIiIxBzbloP528gtQ8jqIZm3oVtGeeeQazZs3CpUuXIIoiRFFEZmYmlixZgvDwcBw6dOi2Xy+KYoPCkmk6k6FGcUUVnG2tEObD9WdEREREUuoS1Az92nhUj6LtPS91HPo/dS5of/75Jz7//HOIoojBgwdj7dq1+PXXX/Hcc8/B0dERqampGDx4MH788cfGzEsmqGZ7/R7BbpDLBInTEBEREVHNWrSfTqZzFM3I1LmgffnllwCAiRMnYvfu3Zg8eTJGjRqF999/H4mJiRg0aBA0Gg0mTZqEr776qtECk+mpOaCa68+IiIiIjEPnwGbo38YDWp2IT/dwFM2Y1LmgHT16FIIgYPHixTd85uvri927d2P27NnQarV44okn8MEHHxg0KJmmSq0OJ1K4/oyIiIjI2NSMom05lY7LeSUSp6EadS5o2dnZcHR0RGBg4E0/FwQBy5Ytw5tvvglRFPHSSy8hKirKYEHJNP1zpRClGi2a2VsjxMtJ6jhEREREdE1EYDMMCKkZReOOjsaizgXN1tYWGo3mjtctWLAAH330EQDg7bffxrx58/QOR6avdv1ZCzfIuP6MiIiIyKjU7Oj486l0pORyFM0Y1LmgtWrVChqNBvHx8Xe8dtasWVi1ahVkMhk+/vhjPP7449DpdA0KSqap9vwzTm8kIiIiMjqdAlwwkKNoRqXOBS0yMhIAsHXr1jpd/+ijj+K7776DlZUVVq1ahZycHL0CkumqqNLixGUWNCIiIiJjNvvaKNrWWI6iGYM6F7RRo0ZBFEWsXLkSlZWVdfqaCRMmYOvWrbC1tdU7IJmuuDQVyit1cHdUoLWno9RxiIiIiOgmOgW4YFCoJ7Q6EZ9wR0fJ1bmgDR06FFOmTEG/fv0QGxtb5weMGDECf/zxBwYMGIB+/frpk5FM1H/PPxMErj8jIiIiMlazB1fv6Lj1VDoucRRNUlZ1vtDKCl9//bVeD+nTpw/27Nmj19eS6YpOzgXA88+IiIiIjF14gAsGh3rir6RsfLrnPD68v5PUkSxWnUfQiOqjvFKLk6mFALj+jIiIiMgUzB7y7yhack6xxGksl8EL2qZNm7B+/XpD37bOFi1ahF69esHe3h4uLi43fB4XF4eJEyciICAAdnZ2CAsLw8cff3zDdZ999hnCwsJgZ2eHkJAQSb8nU3QytQCaKh08nGwQ7O4gdRwiIiIiuoOO/i4YEuYJnQgs546OkjF4QZs1axamTZtm6NvWmUajwYQJE/Dkk0/e9POYmBh4enpiw4YNiI+Px6uvvor58+dj+fLltdd88cUXmD9/Pl5//XXEx8fjjTfewNNPP41ff/21qb4Nk1e7vT7XnxERERGZjNmD/93R8SJH0SRR5zVo9SGKYmPctk7eeOMNAMDatWtv+vn/l8fg4GBER0djy5YteOaZZwAA33zzDR5//HE88MADtdccP34cS5YswZgxYxovvBk5cm2DEE5vJCIiIjIdHfyVGBLmiT8Ts7F8zwUse6CT1JEsDtegAVCpVHB1da3954qKihuOBrCzs8OxY8fqfMSAJSvTaHEqrQAANwghIiIiMjVzrp2L9gtH0SRh8QXt8OHD2LhxI2bOnFn73l133YVVq1YhJiYGoijixIkTWLVqFSorK5Gbm3vT+1RUVECtVl/3slQxlwtQqRXho7RFkJu91HGIiIiIqB7a+ykxJMwLOhH49C+ei9bUTKKgvfzyyxAE4bavpKSket/3zJkzGDduHKKiojBs2LDa91977TWMGDECPXv2hLW1NcaNG4cpU6YAAGSym/9XtnjxYiiVytpXQECAft+sGfjv9vpcf0ZERERkeuZc29FxW1wGLmRzFK0pGbyg+fv7IzAw0KD3fO6555CYmHjbV3BwcL3umZCQgMGDB2PmzJlYsGDBdZ/Z2dlhzZo1KC0tRUpKClJTU9G8eXM4OTnBw8PjpvebP38+VCpV7SstLU3v79fU1RxQ3ZPrz4iIiIhMUns/JYa2vTaKtoejaE3J4JuEHD9+3NC3hIeHxy2LkT7i4+MxaNAgTJkyBYsWLbrlddbW1vD39wcA/PDDDxg9evQtR9BsbGxgY2NjsIymqqSiCv9cUQHg+jMiIiIiUzZ7cGvsTsjCtrgMPDuoNVp5OkodySKYxBTH+khNTUVsbCxSU1Oh1WoRGxuL2NhYFBdXD82eOXMGAwcOxLBhwzBv3jxkZmYiMzMTOTk5tfc4d+4cNmzYgPPnz+PYsWN48MEHcebMGbzzzjtSfVsm43hKPqp0Ivxc7BDgyvVnRERERKaqvZ8Sw9p6QRSBT7gWrcmYXUFbuHAhIiIiEBUVheLiYkRERCAiIgInTpwAAGzevBk5OTnYsGEDfHx8al/dunWrvYdWq8XSpUsRHh6OoUOHory8HIcPH0bz5s0l+q5MR+35Z5zeSERERGTyZl9bi/brPxm4kF0kcRrLIIhSHlpmxtRqNZRKJVQqFZydnaWO02TGfXYIcWmFWDohHPd18Zc6DhERERE10OPfnMAf8VkYE+6LTydGSB3HJNWnG5jdCBpJp6i8EmfSr60/4wgaERERkVmYPbj6XLTt/2TgfBZH0RobCxoZzPGUfGh1IoLc7OHrYid1HCIiIiIygLa+zhjezhuiCHzMtWiNjgWNDKZme33u3khERERkXmrWou04fRXnOIrWqFjQyGCik68VNE5vJCIiIjIrYT7OGNGeo2hNgQWNDEJVWon4DDUAoCdH0IiIiIjMzqzB1aNov52+irOZHEVrLCxoZBBHL+VBFIFgdwd4OdtKHYeIiIiIDCzMxxkjO3jzXLRGxoJGBlFz/llPTm8kIiIiMls1o2g7OIrWaFjQyCBq159xeiMRERGR2Qr1dsaoDj4AOIrWWFjQqMEKSjRIvMr1Z0RERESW4L+jaEmZaonTmB8WNGqwo5eqR89aezrCw8lG4jRERERE1JhCvJ04itaIWNCowWrPP+P6MyIiIiKLMGtwawgC8NvpzNqZVGQYLGjUYFx/RkRERGRZQrydMJKjaI2CBY0aJLe4AueyigEAPVjQiIiIiCzG7GujaL+fyURCBkfRDIUFjRrk6LXt9UO9neDqoJA4DRERERE1lTZeXIvWGFjQqEGik3MBcPdGIiIiIktUM4q2Mz4T8RkqqeOYBRY0ahBuEEJERERkuVp7OWF0R1/8r707j4uq3P8A/plhGdZhQGAEJQxwJXdKcQO3zIzIcsl9yazUytS8/jSvu127N61r1PWq6S0zl9zNLDXJTLREzBXcwB1UZJNd5vn9gXNinBlg0GFm4PN+veb1qjNn+Z7nHPB8+Z7neQBW0R4XJmhUZbeyC3Dxdi5kMqD9k0zQiIiIiGqjd7uHQCYDfjydxiraY8AEjapMO3pjMz8lPFwcLBwNEREREVlCiK87oh5U0T7dyyrao2KCRlV2mMPrExERERGAdx5U0X46k4ZT11lFexRM0KjK2P+MiIiIiIDSKtqLLR9U0dgX7ZEwQaMquZmVj5T0PMhlwNNPelk6HCIiIiKysLe7NYRcBuxhFe2RMEGjKtG+3vhUPQ8ondj/jIiIiKi2C/F1k6pon7AvWpUxQaMqkV5vZP8zIiIiInrg7e6lVbS9Z1lFqyomaFQl2hEc27P/GRERERE9EOzjhuhW9QAAn+w9Z+FobBMTNDLZtYw8XL2bDzu5DE83YP8zIiIiIvrL291CHlTRbuHkNVbRTMUEjUymfb2xRX0PuCnsLRwNEREREVmTIB83vMQqWpUxQSOTxXH+MyIiIiIqx4QHVbR9ibdw4lqmpcOxKUzQyCRCCBx+UEFrzwSNiIiIiAwI8nHDS621VTSO6GgKJmhkkit383AjqwAOdjKENfC0dDhEREREZKW086L9nHgLf17NtHQ4NoMJGplEO/9Zy/oquDiy/xkRERERGfakt6tURft0H6tolcUEjUwizX/G4fWJiIiIqALvdGsIO7kMPyfewnFW0SqFCRpVmhCCA4QQERERUaU18HaVRnT8lCM6VgoTNKq05Du5SMsuhKOdHG0C2f+MiIiIiCr2drcQ2Mll2J90GwlXMiwdjtVjgkaVpq2etX5CBScHOwtHQ0RERES2oIG3K/qyL1qlMUGjSmP/MyIiIiKqCm0VLTbpNo6xilYuJmhUKUIIHL50FwDnPyMiIiIi0wTWccXL2ioa50UrFxM0qpSLt+/hzr1CKOzlaP2EytLhEBEREZGNefvBiI6/nLuN+MusohnDBI0qRft6Y9tATyjs2f+MiIiIiEzzRB0XvNKGfdEqwgSNKoXD6xMRERHRo5rQtSHs5TIcYBXNKCZoVCGN5q/+ZxwghIiIiIiqqrSKVh8A8AnnRTOICRpV6NytHNzNLYKzgx1a1FdZOhwiIiIismETuoXAXi7Dr+fvIP7yXUuHY3WYoFGFtP3Pwhp4wtGetwwRERERVV2Alwv6tdVW0dgX7WF82qYKcf4zIiIiInqcxnf9q4p2NIVVtLKYoFG5NBqBI8mc/4yIiIiIHp8ALxf0D2MVzRAmaFSus6nZyMovhqujHZrX87B0OERERERUQ4yLLK2iHbxwB3+wiiZhgkbl0r7e+PSTXnCw4+1CRERERI9HaRUtAABHdCyLT9xUrsOc/4yIiIiIzGR812DYy2X47UI6fk9mFQ1ggkblKCnT/4wDhBARERHR41bfk1W0hzFBI6NO38hCTsF9uDvZI9Sf/c+IiIiI6PEb3zUYDnYyHLqYjiMP3t6qzZigkVHa/mftnvSCnVxm4WiIiIiIqCYqW0X7dB9HdGSCRkbFPfgLBofXJyIiIiJzGt81hFW0B5igkUHFJRr8wfnPiIiIiKga1FM5Y4DUF612V9GYoJFBp65nIbeoBB7ODmjmp7R0OERERERUw2mraHGX0qWRxGsjJmhkkPb1xnZPekHO/mdEREREZGb+KmcMfJojOjJBI4O0A4RweH0iIiIiqi7jIkPgaCfH4Ut3pefR2oYJGukpuq/B0ZQMAEzQiIiIiKj6sIrGBI0MOHEtE/nFJfBydUQjX3dLh0NEREREtci4rsFwtJPjSPJdHLp4x9LhVDsmaKRHW05uH8T+Z0RERERUvfw8nPHqM3+N6CiEsHBE1YsJGunh/GdEREREZElvRZZW0X5Prn190ZigkY7C+yWIv/yg/xkTNCIiIiKyAD8PZwyqpVU0Jmik4/iVTBTe18DbTYEQXzdLh0NEREREtdRbkSFwtJfj95TaVUVjgkY6/nq90QsyGfufEREREZFl1PVwwuBnngAALNl7rtZU0ZigkQ7Of0ZERERE1uKtyGA42svxR0oGDtWSKhoTNJIUFJcg4UomAPY/IyIiIiLLUyvLVNH21I4qGhM0khy7nIGiEg3USgWe9Ha1dDhERERERFIV7ejlDPx2oeZX0ZigkUTb/yw8qA77nxERERGRVdCpotWCvmhM0Ejy1wTVfL2RiIiIiKzHuMhgKOzliL+cgYMX7lg6HLNigkYAgLyi+/jzWiYADhBCRERERNbFV+mEwe1qR180JmgEAIi/nIHiEgF/Dyc84eVi6XCIiIiIiHS8FVFaRTt2JRO/nq+5VTQmaASgzOuNwex/RkRERETWx1fphCHtAgEAn9TgvmhM0AiA7gAhRERERETW6M3IIKmKdqCGVtGYoBHuFd7HiWtZANj/jIiIiIisl6+7E4a2r9lVNCZohD9S7qJEIxDg5Yz6nux/RkRERETW642IIDg5yJFwJRO/nLtt6XAeOyZohMMX+XojEREREdkGX3cnDJX6op2vcVU0Jmgk9T/j/GdEREREZAveiAiGk4Mcx69mIraGVdGYoNVy2QXFOHWd/c+IiIiIyHb4uCswrH3NrKIxQavl/ki+C40AGtRxgZ+Hs6XDISIiIiKqlLFdSqtof17NRGxSzamiMUGr5bTzn7F6RkRERES2xMddgeHhDQDUrBEdmaDVcux/RkRERES2amyXIDg72OHPa1nYn3TL0uE8FkzQarHMvCKcuZkNgCM4EhEREZHt8XZTYHh4zeqLxgStFjuSfBdCAME+rvBVOlk6HCIiIiIik73+oIp2ooZU0Zig1WLa/md8vZGIiIiIbJW3mwLDO9ScKhoTtFrs8CUOEEJEREREtm9s5yC4OJZW0X5OtO0qGhO0WupubhESU3MAsIJGRERERLatjlvZER1tu4rGBK2WOvKgetZI7QZvN4WFoyEiIiIiejSvd34SLo52OHk9C/vO2m4VjQlaLaUdXp+jNxIRERFRTaBTRdtnu/OiMUGrpThBNRERERHVNGO7lPZFO3U9G3tttIrGBK0Wup1TiPO37kEmA9o9yQSNiIiIiGoGL1dHjOjQAADwyV7brKIxQauFtKM3NqmrhKero4WjISIiIiJ6fF7vHARXRzucvpGNPWfSLB2OyZig1ULa/mftg7wsHAkRERER0eOlW0WzvREdmaDVQoc5QAgRERER1WDaKtqZm9n4ycaqaPaWDoCqV1p2AS7dzmX/MyIiIiKqsTxdHfFmRDAy84vR+gmVpcMxCRO0WkZbPQv1V8LDxcHC0RARERERmcfb3RtaOoQq4SuOtYw0vD5fbyQiIiIisjpM0GoZaYJqzn9GRERERGR1mKDVIjcy83E5PQ92chmebsARHImIiIiIrA0TtFpE+3rjU/U84O7E/mdERERERNaGCVotwvnPiIiIiIisGxO0WoTznxERERERWTcmaLXE1bt5uJaRD3v2PyMiIiIislpM0GoJ7euNLep7wFXB6e+IiIiIiKxRjUvQFixYgA4dOsDFxQUqlUrv+/T0dDz33HPw9/eHQqFAQEAAJkyYgOzsbJ31YmNj0aZNGygUCoSEhGD16tXVcwJmcvgih9cnIiIiIrJ2NS5BKyoqQv/+/fHWW28Z/F4ulyM6Ohrbt2/HuXPnsHr1auzduxdvvvmmtE5ycjL69OmDrl274vjx45g4cSLGjBmDH3/8sbpO47ESQvw1/1mQt4WjISIiIiIiY2RCCGHpIMxh9erVmDhxIjIzMytc99///jf++c9/4urVqwCAv/3tb/j+++9x6tQpaZ1XX30VmZmZ2L17d6WOn52dDQ8PD2RlZUGpVFbpHB6XlDu5iPxXLBzsZDgxqxecHe0sGg8RERERUW1iSm5Q4ypoprpx4wY2b96MiIgIaVlcXBx69Oihs16vXr0QFxdndD+FhYXIzs7W+VgLbfWsdYAnkzMiIiIiIitWaxO0QYMGwcXFBfXq1YNSqcSKFSuk71JTU6FWq3XWV6vVyM7ORn5+vsH9ffjhh/Dw8JA+AQEBZo3fFB7ODggL9ETnhny9kYiIiIjImtlEgjZt2jTIZLJyP4mJiSbtc8mSJTh27Bi2bduGixcvYtKkSY8U4//93/8hKytL+mhfl7QGzzf3w3dvdcDb3RtaOhQiIiIiIiqHTYy3PnnyZIwcObLcdYKCgkzaZ926dVG3bl00adIEXl5e6Ny5M2bOnAk/Pz/UrVsXaWlpOuunpaVBqVTC2dnZ4P4UCgUUCoVJMRAREREREZVlEwmaj48PfHx8zLZ/jUYDoLQfGQCEh4dj165dOuvs2bMH4eHhZouBiIiIiIjIJhI0U1y5cgV3797FlStXUFJSguPHjwMAQkJC4Obmhl27diEtLQ1PP/003NzccPr0abz//vvo2LEjGjRoAAB488038dlnn2Hq1KkYPXo0fv75Z2zYsAHff/+95U6MiIiIiIhqvBo3zP7IkSPxv//9T2/5/v37ERkZif3792PGjBk4c+YMCgsLERAQgJdffhnTpk3Tmdg6NjYW7733Hs6cOYP69etj5syZFb5mWZY1DbNPRERERESWY0puUOMSNGvBBI2IiIiIiADOg0ZERERERGSTmKARERERERFZCSZoREREREREVoIJGhERERERkZVggkZERERERGQlmKARERERERFZCSZoREREREREVoIJGhERERERkZVggkZERERERGQlmKARERERERFZCSZoREREREREVoIJGhERERERkZVggkZERERERGQlmKARERERERFZCSZoREREREREVoIJGhERERERkZVggkZERERERGQlmKARERERERFZCSZoREREREREVoIJGhERERERkZWwt3QANZUQAgCQnZ1t4UiIiIiIiMiStDmBNkcoDxM0M8nJyQEABAQEWDgSIiIiIiKyBjk5OfDw8Ch3HZmoTBpHJtNoNLhx4wbc3d0hk8nMdpzs7GwEBATg6tWrUCqVZjtObcY2Nj+2sfmxjc2L7Wt+bGPzYxubH9vYvKy5fYUQyMnJgb+/P+Ty8nuZsYJmJnK5HPXr16+24ymVSqu7EWsatrH5sY3Nj21sXmxf82Mbmx/b2PzYxuZlre1bUeVMi4OEEBERERERWQkmaERERERERFaCCZqNUygUmDVrFhQKhaVDqbHYxubHNjY/trF5sX3Nj21sfmxj82Mbm1dNaV8OEkJERERERGQlWEEjIiIiIiKyEkzQiIiIiIiIrAQTNCIiIiIiIivBBI2IiIiIiMhKMEGzATExMWjQoAGcnJzQrl07/P7775Xabt26dZDJZHjppZfMG2ANYEobr169GjKZTOfj5ORUjdHaJlPv48zMTIwfPx5+fn5QKBRo1KgRdu3aVU3R2iZT2jgyMlLvPpbJZOjTp081RmxbTL2HP/nkEzRu3BjOzs4ICAjAe++9h4KCgmqK1jaZ0sbFxcWYO3cugoOD4eTkhJYtW2L37t3VGK1tOXDgAKKiouDv7w+ZTIatW7dWuE1sbCzatGkDhUKBkJAQrF692uxx2jJT2/jmzZsYPHgwGjVqBLlcjokTJ1ZLnLbM1DbevHkzevbsCR8fHyiVSoSHh+PHH3+snmAfARM0K7d+/XpMmjQJs2bNwrFjx9CyZUv06tULt27dKne7lJQUTJkyBZ07d66mSG1XVdpYqVTi5s2b0ufy5cvVGLHtMbWNi4qK0LNnT6SkpOC7775DUlISli9fjnr16lVz5LbD1DbevHmzzj186tQp2NnZoX///tUcuW0wtX3Xrl2LadOmYdasWTh79ixWrlyJ9evXY/r06dUcue0wtY0/+OADLFu2DEuXLsWZM2fw5ptvom/fvkhISKjmyG1Dbm4uWrZsiZiYmEqtn5ycjD59+qBr1644fvw4Jk6ciDFjxtjEw62lmNrGhYWF8PHxwQcffICWLVuaObqawdQ2PnDgAHr27Ildu3YhPj4eXbt2RVRUlPX/nhBk1Z555hkxfvx46f9LSkqEv7+/+PDDD41uc//+fdGhQwexYsUKMWLECBEdHV0NkdouU9t41apVwsPDo5qiqxlMbeMvvvhCBAUFiaKiouoK0eZV5XdFWUuWLBHu7u7i3r175grRppnavuPHjxfdunXTWTZp0iTRsWNHs8Zpy0xtYz8/P/HZZ5/pLHv55ZfFkCFDzBpnTQBAbNmypdx1pk6dKkJDQ3WWDRw4UPTq1cuMkdUclWnjsiIiIsS7775rtnhqIlPbWKtZs2Zizpw5jz+gx4gVNCtWVFSE+Ph49OjRQ1oml8vRo0cPxMXFGd1u7ty58PX1xWuvvVYdYdq0qrbxvXv3EBgYiICAAERHR+P06dPVEa5Nqkobb9++HeHh4Rg/fjzUajWeeuopLFy4ECUlJdUVtk2p6n1c1sqVK/Hqq6/C1dXVXGHarKq0b4cOHRAfHy+9onfp0iXs2rULzz//fLXEbGuq0saFhYV6r5c7Ozvj4MGDZo21toiLi9O5HgDQq1evSv9OIbJGGo0GOTk58PLysnQo5WKCZsXu3LmDkpISqNVqneVqtRqpqakGtzl48CBWrlyJ5cuXV0eINq8qbdy4cWN8+eWX2LZtG9asWQONRoMOHTrg2rVr1RGyzalKG1+6dAnfffcdSkpKsGvXLsycORMff/wx5s+fXx0h25yqtHFZv//+O06dOoUxY8aYK0SbVpX2HTx4MObOnYtOnTrBwcEBwcHBiIyM5CuORlSljXv16oXFixfj/Pnz0Gg02LNnj/TqLj261NRUg9cjOzsb+fn5FoqK6NH861//wr179zBgwABLh1IuJmg1SE5ODoYNG4bly5fD29vb0uHUWOHh4Rg+fDhatWqFiIgIbN68GT4+Pli2bJmlQ6sxNBoNfH198d///hdt27bFwIEDMWPGDPznP/+xdGg10sqVK9G8eXM888wzlg6lxoiNjcXChQvx+eef49ixY9i8eTO+//57zJs3z9Kh1RiffvopGjZsiCZNmsDR0RETJkzAqFGjIJfz0YaI9K1duxZz5szBhg0b4Ovra+lwymVv6QDIOG9vb9jZ2SEtLU1neVpaGurWrau3/sWLF5GSkoKoqChpmUajAQDY29sjKSkJwcHB5g3axpjaxoY4ODigdevWuHDhgjlCtHlVaWM/Pz84ODjAzs5OWta0aVOkpqaiqKgIjo6OZo3Z1jzKfZybm4t169Zh7ty55gzRplWlfWfOnIlhw4ZJVcnmzZsjNzcXY8eOxYwZM5hEPKQqbezj44OtW7eioKAA6enp8Pf3x7Rp0xAUFFQdIdd4devWNXg9lEolnJ2dLRQVUdWsW7cOY8aMwcaNG/Ve3bVG/BfCijk6OqJt27bYt2+ftEyj0WDfvn0IDw/XW79JkyY4efIkjh8/Ln1efPFFaQSmgICA6gzfJpjaxoaUlJTg5MmT8PPzM1eYNq0qbdyxY0dcuHBB+gMDAJw7dw5+fn5Mzgx4lPt448aNKCwsxNChQ80dps2qSvvm5eXpJWHaPzgIIcwXrI16lHvYyckJ9erVw/3797Fp0yZER0ebO9xaITw8XOd6AMCePXsq/W8jkbX49ttvMWrUKHz77be2M5WMpUcpofKtW7dOKBQKsXr1anHmzBkxduxYoVKpRGpqqhBCiGHDholp06YZ3Z6jOFbM1DaeM2eO+PHHH8XFixdFfHy8ePXVV4WTk5M4ffq0pU7B6pnaxleuXBHu7u5iwoQJIikpSezcuVP4+vqK+fPnW+oUrF5Vf1d06tRJDBw4sLrDtTmmtu+sWbOEu7u7+Pbbb8WlS5fETz/9JIKDg8WAAQMsdQpWz9Q2Pnz4sNi0aZO4ePGiOHDggOjWrZt48sknRUZGhoXOwLrl5OSIhIQEkZCQIACIxYsXi4SEBHH58mUhhBDTpk0Tw4YNk9a/dOmScHFxEe+//744e/asiImJEXZ2dmL37t2WOgWrZ2obCyGk9du2bSsGDx4sEhIS+DxRDlPb+JtvvhH29vYiJiZG3Lx5U/pkZmZa6hQqhQmaDVi6dKl44oknhKOjo3jmmWfE4cOHpe8iIiLEiBEjjG7LBK1yTGnjiRMnSuuq1Wrx/PPPi2PHjlkgatti6n186NAh0a5dO6FQKERQUJBYsGCBuH//fjVHbVtMbePExEQBQPz000/VHKltMqV9i4uLxezZs0VwcLBwcnISAQEBYty4cUweKmBKG8fGxoqmTZsKhUIh6tSpI4YNGyauX79ugahtw/79+wUAvY+2TUeMGCEiIiL0tmnVqpVwdHQUQUFBYtWqVdUety2pShsbWj8wMLDaY7cVprZxREREuetbK5kQfNeCiIiIiIjIGrAPGhERERERkZVggkZERERERGQlmKARERERERFZCSZoREREREREVoIJGhERERERkZVggkZERERERGQlmKARERERERFZCSZoREQ2YvXq1ZDJZIiMjLR0KDXOH3/8gaioKHh7e0Mul0Mmk2H27NmWDsvsRo4cWWvO1ZAGDRpAJpMhNjbW0qEQkRkcOHAAUVFR8Pf3h0wmw9atW816vNmzZ0Mmk+l8mjRpYvJ+mKARET0wYsQIyGQytGnTptLbDB8+HDKZDO3atTNjZGRO58+fR2RkJHbu3ImMjAx4e3tDrVbDzc3N0qEREdEjyM3NRcuWLRETE1NtxwwNDcXNmzelz8GDB03eBxM0IqIHhg0bBgBISEjA2bNnK1w/Ly8PW7ZsAVCaqJmbh4cHGjdujCeeeMLsx6pN/vvf/yIvLw+dO3dGeno6bt26hdTUVEyZMsXSoRER0SPo3bs35s+fj759+xr8vrCwEFOmTEG9evXg6uqKdu3aPXJF3d7eHnXr1pU+3t7eJu+DCRoR0QPdunVDvXr1AABff/11hetv2bIF9+7dg4ODAwYOHGju8NC3b18kJibiq6++MvuxapPTp08DAAYMGACVSmXZYIiIqNpMmDABcXFxWLduHU6cOIH+/fvjueeew/nz56u8z/Pnz8Pf3x9BQUEYMmQIrly5YvI+mKARET0gl8sxZMgQAMDatWshhCh3fW0S17t37yr9hYysQ35+PgDwlUYiolrkypUrWLVqFTZu3IjOnTsjODgYU6ZMQadOnbBq1aoq7bNdu3ZYvXo1du/ejS+++ALJycno3LkzcnJyTNoPEzQiojK0rypevnwZv/76q9H10tLSsHfvXp1tcnJysGrVKvTr1w/NmjWDu7s7XF1dERoaiqlTp+L27dsG9xUbGwuZTIYGDRoAAHbs2IGePXvC29tbp1NzeYOEXL16FYsWLcKzzz6L4OBgODk5QaVSoUOHDli6dCmKiooMHlvboXnkyJEAgJUrVyIsLAxubm5QqVR47rnncOTIkXLb7NatW5g+fTpatmwJpVIJNzc3NG3aFCNHjsTPP/9stP2mTp2K0NBQuLq6ws3NDa1atcK8efNM/oesrD/++AOvvvoq/P39oVAooFarER0djX379umtGxkZqTNAxKhRo6RO3dprUZHKXrvCwkKsX78eQ4cORfPmzeHp6QlnZ2c0bNgQ48aNQ0pKisH9p6SkSDEBwJ9//ol+/frB19cXzs7OaN68OT755BNoNBqjMSYnJ2Po0KHw9fWFi4sLQkND8c9//hMlJSUVnt+NGzfw7rvvomHDhnB2doanpyc6deqE5cuXG92+7MAb169fx+uvv4769evDxcUFLVq0wOrVq6V1NRoNYmJi0Lp1a7i6usLHxwejRo3CrVu3KozNkGPHjmHIkCEIDAyEQqGAUqlESEgIoqOjsWzZsnLbyZBz587htddek/bn7e2NZ599Fhs3bjS6jfZ6paSk4OTJk+jfvz/UarXO9aqo7bds2YIXXngBarUajo6O8PPzwyuvvFKlvixEZNjJkydRUlKCRo0awc3NTfr88ssvuHjxIgAgMTFRb9CPhz/Tpk2T9tm7d2/0798fLVq0QK9evbBr1y5kZmZiw4YNpgUniIhIR+vWrQUA8frrrxtdZ8mSJQKAUKlUoqCgQAghxNKlSwUAAUDY29sLLy8vYWdnJy2rX7++uHjxot6+9u/fLwCIwMBAsWjRIgFAyGQy4enpKeRyudiyZYsQQohVq1YJACIiIkJvH6+88op0HCcnJ+Hp6Sn9PwARGRkpCgsL9babNWuWACBGjBghRo4cKcXu5uYmbatQKMSvv/5qsB327t0rPDw8dNb19PQUMplMOqeHxcbGCpVKpROvo6Oj9P9NmjQR169fN9r2xsTExEjHlclkQqVSCblcLu13+vTpOuv37dtXqNVq4eDgIAAIpVIp1Gq1UKvVIiwsrFLHrOy127FjhxSHXC4XXl5e0nG199GRI0f09p+cnCyt88MPPwgnJycBQHh4eEjnCkCMHz/eYHzx8fFCqVRK6ymVSum40dHRYvjw4QKAmDVrlt62hw4d0rlOSqVS5zr17NlT5Obm6m0XGBgoAIgvv/xSqNVqg/EuWrRIaDQa0a9fP+m+cXZ2lr4PDQ0V+fn5lboGWjt27BD29vbSPlxcXISrq6vOz8HD+9TGun//fr39bdmyRSgUCp1rVHb/w4cPFyUlJXrbab//+uuvhYuLi3T+Za/3iy++KIqLi/W2LSwsFAMHDtSJuez1k8lk4l//+pdJ7UJEpQBIv5OFEGLdunXCzs5OJCYmivPnz+t8bt68KYQo/Zk8e/ZsuZ9bt26Ve9ywsDAxbdo002I1+eyIiGo4bfLl6ekpJV8Pa9OmjQAgxo4dKy1bt26dmDlzpjh27Jj08FVcXCwOHTokOnToIACI7t276+1L+5Dv5OQk7OzsxLvvvitu374thBAiKytLpKWlCSHKT9BmzpwpYmJixMWLF4VGoxFCCJGXlyc2bNgg6tWrJwCIefPm6W2nTdBUKpVwcXERK1askB5iT58+LVq0aCEAiLZt2+ptm5iYKCVy7du3FwcPHpSOnZOTI7Zu3SpGjx6ts82lS5eEUqkUMplMTJw4USQnJwuNRiPu378vjhw5Itq1aycAiG7duhlsd2MOHDggJWPDhg2T/nG9e/eumDRpkvSAu2HDBr1tIyIiBACxatUqk44pROWvXWxsrHjvvffEoUOHpHuqpKREnDhxQrzwwgsCgGjUqJHeA3/ZBE2lUokhQ4aIq1evSvvXnptMJhMnTpzQ2TY/P1+EhIQIAOKpp54S8fHxQgghCgoKxOeffy4cHByk5PrhBC09PV1KrsLCwsSff/4phCh9WPnyyy+lRHHcuHF6baJNejw8PESnTp3EmTNnhBBCZGdni7ffflsAEM7OzmLGjBlCqVSKb7/9VhQVFYmSkhLx/fffSwnJp59+atK1aNCggQAgRo8eLa5cuaJzLj/88IMYNGiQ3h8pjCVo58+fl5KrXr16SX9Yyc3NFYsWLZLutY8++kgvDu318vDwEO3bt5fOPz8/X/z73/+WkryFCxfqbattn6ZNm4pt27aJvLw8IYQQGRkZ4sMPPxSOjo5CJpOJ2NhYk9qGiPQTtKSkJAFAHDhwwGzHzMnJEZ6enib/PmOCRkT0kNTUVOkhatOmTXrfnzlzRnoIO3jwYKX2mZGRIXx9fQUAceHCBZ3vtA/5AMTQoUON7qO8BK08v/32m1TBe5g2QQMgli9frvd9QkKC9H1ycrLOd3379hUAROvWrStd7Rg8eLDRZFGI0oTK399fADBYUTImMjJSqupok8Sy+vfvLwCIxo0b633/OBK0iq5deQoLC0VoaKgAIPbu3avzXdkErWPHjga3b9mypcEka+XKlQKAcHV1lZK6sj766CNp3w9vO3v2bAFA+Pr6ivT0dL1tY2JiBABhZ2enkwwJ8VfS4+XlJTIzM3W+02g0olGjRtJx16xZo7fvefPmmXyfp6WlSed6//79Sm9nLEHTVpNDQ0MN/pHm/fffl5Lmh6uI2nNTq9UiIyNDb9uFCxdKCZw2AROi9GFRJpMJf39/kZqaajBebZW2d+/elT5HotosJydHJCQkSP+WLV68WCQkJIjLly8LIYQYMmSIaNCggdi0aZO4dOmSOHLkiFi4cKHYuXNnlY43efJkERsbK5KTk8Vvv/0mevToIby9vSussj2MfdCIiB6iVqvx7LPPAgDWrFmj9712WVBQEDp27FipfapUKoSHhwMADh8+bHS9yZMnmxpuhTp06ACVSoVr167h+vXrBtfx9/fHqFGj9Ja3atUK9evXB/DXaIdAaX+77du3AwDmz58PJyenCuPIy8vDxo0b4eDggHfeecfgOp6enujduzcAGOw3Zkh6errUj2zGjBlSf62ypk+fDgBISkrCqVOnKrVfU1X12jk6OqJHjx4Ayr83PvjgA4PLo6KiAOheHwDYvHkzAGDw4MHSNSxr/PjxcHV1NbjPTZs2AQDGjRsHLy8vve9fe+01qNVqlJSUGJ349c0334SHh4fOsrJ9KAMCAjBo0CC97bp3727wfMrj5uYGmUyG4uJipKenV3o7Q4QQ0vQZ77//PhQKhd46kydPhkKhQGZmptH79K233jI4Kug777wDFxcXZGVlSf1YAeCrr76CEAJDhw6FWq02uM/BgwcDKO37WJk+hES13dGjR9G6dWu0bt0aADBp0iS0bt0af//73wEAq1atwvDhwzF58mQ0btwYL730Ev74448qT2dz7do1DBo0CI0bN8aAAQNQp04dHD58GD4+PibthwkaEZEB2oE/du3ahYyMDGm5EALffPMNAGDo0KF62yUnJ2PixIlo0aIF3N3dIZfLpY7E27ZtAwDcvHnT4DGdnZ3RokWLKsd88OBBDB06FMHBwXBxcdHpxJyZmVnusUNDQ2FnZ2fwO+3UA9p9AKX/6JWUlMDBwUF6oK5IfHw8iouLodFo0KhRI515Ysp+1q1bB6B04JPKSEhIAFCa6HTo0MHgOq1atYKnp6fO+o9TZa7drVu38MEHHyAsLAwqlQp2dnbS9fn0008BGL8+AIzu39D1AYDjx48DALp06WJwOxcXF7Rt21ZveVFRkZQcde3a1eC2CoVCamtj7fnUU08ZXO7r6wsAaNasGeRy/ccQ7fcPn095XFxc0KVLFxQVFSE8PBxLlixBYmJihSOxGnLx4kVkZWUBMH7+arUazZo1A2D8/CMiIgwud3V1RVhYmN62cXFxAIBly5YZ/dnQbpefn//IiShRbRAZGQlR+sagzkc7WJGDgwPmzJmD5ORkFBUV4caNG9i8eTOaN29epeOtW7cON27cQGFhIa5du4Z169YhODjY5P3YV+noREQ1XHR0NJRKJbKzs7Fhwwa88cYbAIBff/0Vly9fBvDXxNZa+/btw4svvoi8vDwApcP2q1QqODo6AgCysrJQUFCA3Nxcg8esU6eOwQfWyli4cCFmzJgh/b+DgwO8vLzg4OAAALh9+zY0Go3RY/v7+xvdt7Y6VlxcLC3TjrKnVqsNVhgM0SYfJSUlSEtLq3B9bTtW5M6dOwBKH+y152tIYGAgMjIyjI6m+SgqunYnT55Et27dpFiB0onHtW1779495ObmGr0+gPFrZOj6AH+1S3nX1tB3d+/elUY71CZ/hgQGBgKA0fb08/MzuFz7h4C6deuW+/39+/eNHtuQFStW4IUXXkBSUhImTZqESZMmwcvLC927d8fw4cPxwgsvVGo/Za9RReefkJBg9Pwr0+5lt9X+fGRlZUkJYnkq+/NBRLaHFTQiIgOcnJzQv39/ALqvOWrnPgsPD0dISIi0vKioCMOHD0deXh4iIyMRFxeHgoIC3L17F6mpqUhNTUW/fv0AwOhf9Y1VsCpy8uRJzJw5E0DpK2lJSUkoKChAenq6dGztA2FVKgqPS9mHfkN/0TT2F87KKiwsNEPUlVPRtRs9ejTu3LmD5s2bY9++fcjLy0NmZqZ0fd577z0Alr0+hliyTU0VEhKCkydPYtOmTXjttdfQqFEj3L17Fxs3bkRUVBSioqJMHma/Os9fG9vy5csr9fNR2akgiMj2MEEjIjJCWyH77bffkJKSgsLCQnz33Xc632nFxcXhxo0bcHV1xY4dO9C+fXu9ak5V53aqyObNm6HRaBAREYGYmBg0atRIp5pTUlLy2F+H0vaRSUtLq/RDrHabW7duPdYHX+27/bdv30ZBQYHR9bSVT1P7Ajyqy5cv4+jRowCA7du3o1u3bnB2dtZZxxz3hnby9PJem7xx44beMi8vL+n+uXLlitFtLdWe5XFwcMDLL7+MFStWICkpCVeuXMHMmTMhl8uxc+dOLF++vMJ9lD2fRzl/Q2378Hdlt9X+fJR3TCKqHZigEREZ0aVLFwQGBkr9znbu3InMzEw4Ojpi4MCBOutqB99o0qQJ3Nzc9PaVn59f4YTPVaU9trZ/ysOOHDmC/Pz8x3rMtm3bwt7eHsXFxZUezCMsLEzapuzgCI+qVatW0n9rBwt52PHjx6W+hNrO4tVFe33q1KljtOphLO5HoT3PAwcOGPw+Pz8f8fHxessdHR0RGhpablyFhYU4dOiQznGsUUBAAObOnSsNrvHLL79UuE1QUJA0uImx809LS8OZM2cAGD9/Y+2el5cntXvZbdu3bw8A+OGHHyqMkYhqNiZoRERGyGQyaSCQb775Rnq9sU+fPnoj2ymVSgCQKm0P+/jjjyvVr6QqtMdOSkrS+06j0WD27NmP/Zju7u546aWXAJSOnFhe5arsNi+//DKA0lEVy+tDk5+fX+kqW506daTBHBYtWmRwnYULFwIAGjduXOXO31WlvT5379412F9pzZo1OHfu3GM/bt++fQEAa9euNVjN+eKLL4z2edO+jrts2TKDg3WsXLkSaWlpsLOzk45jScXFxeW+HqqtWFbmPpXJZNJ9unjxYhQVFemt8/HHH6OwsBAqlcroIDn/+c9/DP7Mf/bZZ8jNzYVKpZJG7wSAESNGQCaT4ejRo9JARMaUHbiIiGoeJmhEROXQjuZ49uxZ7NixA4D+641A6VD2Tk5OSE9Px+jRo6UH8aysLMydOxd///vfDQ5X/jhoHxB37tyJxYsXS4lNSkoKBgwYgAMHDhgdTv1RLFiwAK6urjh+/Di6deuGQ4cOSQ/J9+7dw/r16/VGuvzHP/4BT09PnDhxAl26dMHPP/8sDReu0Whw+vRpzJ8/H8HBweW+mvewuXPnQi6XIzY2FqNHj5YGIcnIyMDkyZOxceNGAMC8efMex6mbpFmzZvDz84MQAkOGDJFejcvLy8Pnn3+OMWPGmOXeGDx4MIKDg3Hv3j307t1bGtWxqKgIy5Ytw7Rp0/SGwdeaMGEC1Go1MjMz8dxzz+HkyZMAShOhVatWSVMKvPHGGwaH8K9up0+fRvPmzbF06VJcuHBBWl5QUIBVq1bhq6++AgD06tWrUvubPn06XFxccP78efTt2xcpKSkASq/ZRx99hI8//lhnPUPy8vLw/PPPIzExUYolJiZGGsxn6tSpOq+6NmvWTJp+YuTIkZgzZw5SU1Ol7zMyMrBt2zZER0dj0qRJlToPIrJRVZqFjYioFnnmmWekyWe9vLxEYWGhwfX+8Y9/SOvhwSS2crlcmsR4xIgRBicF1k52HBgYWG4cxiaq1mg0onfv3tJx5XK5UKlU0n8vW7bM6IS82omqR4wYYfS45U3kvGfPHqFUKqVjOzk5CS8vL+m8DZ1TXFycUKvV0jaOjo6iTp06wsHBQaf9UlJSym2Ph3322WdCJpMJAEImkwlPT08pDgBi+vTpJp9fRSp77dauXSvFhgeTFGsnQ4+MjBTTp083eB3KTlRtTHkTmMfHx+tcH6VSKRwdHQUAER0dLYYPH27wnhRCiEOHDgkPDw+dmLXbAhA9evTQm6RZCOOTP2tVdM9V5pwfVnZC9bL3Ydk279Onj94k1uXFumXLFp3zValU0jUDIIYNGyZKSkr0ttN+//XXXwsXFxdp27L3d1RUlCguLtbbtri4WIwZM0bv90jZawhAjBw5stJtQ0S2hxU0IqIKaKtoADBw4EBp2PyH/e1vf8OaNWsQFhYGhUIBjUaDsLAwLFu2TPoLvjnIZDJs3boVs2bNQkhICOzs7GBvb4/evXtjz549GDt2rNmO3aNHDyQmJmLKlCnSvFbFxcVo1KgRRo8ejf/9739627Rv3x5JSUlYsGAB2rVrB2dnZ2RmZsLd3R3t27fH1KlTcfToUWkY98oaP348Dh8+jAEDBkCtVuPevXvw8vJCVFQU9uzZgwULFjyu0zbZoEGDsGvXLnTp0gWurq64f/8+mjVrhkWLFuGnn34qd3qAR9GmTRskJCRg8ODB8PHxQVFREUJCQrBo0SJs2rTJ4KTeWuHh4Th9+jTefvttBAcHo6CgAE5OTujQoQOWLVuG3bt3G60eVbemTZviu+++w9ixY9GqVSu4u7sjOztbGmZ/9erV2L59u0kjpb700ks4ceIERo0ahYCAAOTl5cHd3R3du3fH+vXr8dVXX5U7tUKnTp0QFxeHV155BQ4ODpDL5XjqqaewZMkSbNmyBfb2+jMd2dvbY/ny5YiNjcWgQYOk4xYVFSE4OBj9+vXDl19+iaVLl1apnYjINsiEsLIxfYmIiIhslDbpTU5O5lD4RFQlrKARERERERFZCSZoREREREREVoIJGhERERERkZVggkZERERERGQl9IcQIiIiIqIq4dhrRPSoWEEjIiIiIiKyEkzQiIiIiIiIrAQTNCIiIiIiIivBBI2IiIiIiMhKMEEjIiIiIiKyEkzQiIiIiIiIrAQTNCIiIiIiIivBBI2IiIiIiMhKMEEjIiIiIiKyEv8Pm5QzC6ww+FkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "re = mdf.cov_re.iloc[1, 1]\n",
    "with warnings.catch_warnings():\n",
    "    # Parameter is often on the boundary\n",
    "    warnings.simplefilter(\"ignore\", ConvergenceWarning)\n",
    "    likev = mdf.profile_re(1, \"re\", dist_low=0.5 * re, dist_high=0.8 * re)\n",
    "\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.plot(likev[:, 0], 2 * likev[:, 1])\n",
    "plt.xlabel(\"Variance of random slope\", size=17)\n",
    "lbl = plt.ylabel(\"-2 times profile log likelihood\", size=17)"
   ]
  }
 ],
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